They are different people. Liam is a human. Angelus is a demon. Angel is a human in control of a demon body with a demon inside of him and memories of being a demon.
Liam was a lot more complex than people assume from the most vapid reading of the flashbacks. There are hints of it.
The biggest one being the line about wanting to the see the world and Angel telling Buffy how he wished to meet someone interesting (which explains why he went looking in all the wrong places), but this is at the stage where Liam is so unfulfilled by his life (there are lots of hints of that) that he's in a full downward spiral. As Liam says, he feels he can never get his father's approval, so he lives down to every low his father expects of him. He also hints in Spin the Bottle that religious hypocrisy of some sort is an issue Liam had with his father. It's mentioned that Liam's father is a middle class silk and linen merchant (has pretensions that Liam calls him out on concerning multiple servants instead of their one and eating with his hands despite owning silverware--note that provided tableware, rather than a B.Y.O. knife or a cadena pouch, was still a relatively new thing in the 18th century with the fork not even having widespread use until the 18th-19th centuries--it was still deemed unmanly by some). If Liam wanted to travel the world and pursue art, culture and languages (which appear to have been his talents and interests), he would have been very smothered if he were being forced into his father's business and staying in Galway. We do see that Liam has a heart, as he cares about his sister, Kathy. Liam was looking for a way out of Galway and we see that in his words to Darla.
Of course, we also see Liam's father as a disappointed father with an out-of-control son (how much of it is due to him being stifled and unable to get any support for what he wanted for himself?), which Angel later sees the other side of when he's father to Connor.
Liam was even less aware of what was happening to him than William was. Liam, focused on the beautiful stranger offering to show him her world, trustfully didn't even have his eyes open when Darla bit him (as surly as he was a moment before when he was drunkenly plotting to steal silver, hints of Angel's thoughtful, sweet demeanor and a certain yearning innocence in Liam actually does come out in his final moments when speaking to Darla about what he wants), whereas William was looking right at Drusilla's game face and was still taken in by her, even if he was more vocal about how the biting hurt. Of all the Fanged Four, Liam had the least idea of what was happening to him. Darla was the only one who willingly seemed to want the Master's offer, as she was so afraid of death and had no concern for people who had never loved or cared for her. Liam's trustfulness is later seen with Angel trusting Buffy when she also tells him to close his eyes, while he naively has no idea of what is going on and can't remember anything Angelus has done in his body for 4 months.
Angel, much like Liam, still does have a weakness for strong, interesting women, while seemingly having very low opinions of those who are "dumb as a post" or "simpering morons". This is why he was first entranced by Darla and then by Buffy.
But unlike bad girl Darla (a former syphilitic prostitute behind all of that glamorous, high-class finery and staying in the best hotels with a view), Buffy is the complete opposite. Buffy is a good girl (even something of a goody-two-shoe) who wants to help people. Although pure and virginal, she's worldly and smart in the modern L.A. teenager sort of way. She might not be academically brilliant, but she has imagination that serves her well as a Slayer. Her fight to retain her normal human life despite it all is also inspiring to Angel and he does a lot of things to support this, even if it means not being with him. He's the boyfriend who takes her to the ice rink to connect her to her pre-Slayer human life. He's the boyfriend who wants her to have every human thing he can't give her (such as the children he wants and can't have--Angel makes it clear as early as Bad Eggs how much he wants to be a father and how much it bothers him that he can't be). Angel is so inspired by her humanity that he wants to turn himself into the champion of it. He is not only in love with Buffy, but, through her, all of humanity.
As Angel even said to Buffy in Amends, it's not the demon she's at risk from so much as the human man who wants her. Angel is less concerned by his vampire drive to feed than his human drive (Liam's weakness) when it comes to Buffy. Angel is better at holding back the demon who is not him than the human man he really is.
Another thing about his attraction to Buffy... Unlike Spike, Angelus had no interest in Slayers. Angelus had no interest in a strong victim who makes a point to destroy every bit of her humanity to become nothing but a fighting machine. That's Spike's M.O. to be interested in a physical challenge. For Angelus, there's nothing human there to break psychologically. Darla, who fears death after coming so close to it as a human, would also want to stay far away from the vampire's equivalent of a bogeyman and this explains her response to Buffy's reveal.
That's why Angel was so shocked at what Whistler showed him when he saw Buffy. As Angel says, he thought she'd "be bigger, or muscles and all that." Instead, he sees a young girl getting her world stripped away from her: losing her normal high school life, her friends, struggling to stake her first vampire, her parents' marriage collapsing and Buffy all breaking down before his eyes. What Angel saw was the exact opposite of what a Slayer is supposed to be. Slayers were supposed to be Kendra: taken away from their families and raised to be nothing but killing machines with no human earthly connections like friends, family or relationships. Buffy broke all of those rules and fiercely fought against losing her humanity (though she seemed to start giving up on it in BtVS season 5). Angel, who also broke all the rules of what he was, also saw himself having his whole world and everything he had ever known taken from him in an instant, losing everything, having no friends and then getting dumped with a destiny he didn't ask for (both becoming a vampire and getting a soul against his will, just as Buffy was chosen against her will). Angel had no interest in Buffy because she was the Slayer, but because he saw a sad, human girl whom he wanted to help and didn't think she should be suffering alone. Angel could relate to being the only one of your kind in the world and feeling alone. He empathized with her.
And yet, that girl was giving up everything she had ever known because she still wanted to help people. Buffy restored Angel's faith in humanity and was the first person to still want to be his friend and love him even after knowing what he was. Angel was terrified of anyone finding out what he was, because it had gone horribly wrong before (like being hanged in the Hyperion's lobby the last time he tried to help someone). It's no wonder that he thought he could only help Buffy as long as she didn't know. He was always waiting for the inevitable scream, accusations of him being a monster and rejection. In the prior century, all of his efforts to fit back into both vampire and human societies had failed miserably.
I've seen bizarre criticism (usually with a slam on DB's acting, when he's clearly acting exactly what is called for) of Angel acting differently in Welcome to the Hellmouth. Yet, we see the façade of Angel pretending he has it together and is in any way suave and confident when that mask completely collapses as soon as Buffy asks him whether he knows what it is like to have a friend in The Harvest and he can't answer. It's not 1x07 that the façade breaks down, but actually The Harvest's mausoleum scene and that's actually when Buffy seems to actually start to like him (the real him she empathizes with after losing all of her friends, not the confident image he thought she might like better). His behavior in Welcome to the Hellmouth is a lie. His line about how he perceived Slayers to be is actually backed up by Angelus' warning to Spike in Fool for Love. His lines in Helpless and flashback in Becoming, pt. 1 don't actually contradict that he expected someone bigger and stronger than Buffy, as that's exactly what he thought big, scary Slayers were supposed to be before he saw her. It's just that it was half a year earlier that his preconception was completely undone. He doesn't explicitly say that Welcome to the Hellmouth is his first time seeing her and that's not a continuity error.
While Liam might have been very debauched, there's evidence that Angel really had never experienced anything like love until he was with Buffy. It was as new for him as it was her. He also had a lot of innocence to lose.
There's a reason Angel would still consider Liam a victim, no matter how he's perceived as somehow 'asking for it' because he was so flawed. Angel might feel guilt for Liam's flaws creating Angelus, but he still views Liam as a victim who had his entire world crashed down on him, especially when he was dumped back in a demon's body 145 years later and forced to cope with Angelus' memories of crimes. While Liam certainly had issues with Catholic hypocrisy, he was still a Catholic, himself. We see Angel constantly seeking cosmic forgiveness and being very humble in the presence of churches (it seems to go beyond vampire fear) and a real problem with the fact that vampirism is damnation. There's an interesting moment particularly in I Got You Under My Skin where his reaction to Jesus on the cross and the nun are both noteworthy. Angel seems to be very afraid of where he is destined to go when he dies because of his religious background, which is why he is so much more focused on cosmic forgiveness. His preoccupation with this is way beyond Darla or Spike's when they also have their souls.
