I wouldn't even compare Alien and Aliens. They don't even feel like a part one and part two, they are completely different movies.
I wouldn't go that far. I do agree that they are very different movies in terms of tone and directorial style (which isn't surprising since Ridley Scott and James Cameron are very different directors), and the original is more of a classic suspense/horror flick that just happens to be set in space, whereas the second is more of an action flick that just happens to be set in space.
But
Aliens builds on the story and universe established in
Alien. Only one character survived the original, but she's back and is exactly the same character. Some sequels are "more of the same" and some are "let's take things further" and
Aliens is the second type. We only got a piece of the background of the xenomorph and its life cycle; now we have more. There's also Weyland-Yutani ("the company") which is back and being the same asshole corporation they were before.
To me, they feel very much like Part One and Part Two of the same story, as long as one understands that Part Two expands considerably upon Part One.
I feel the same way about the
Toy Story movies. The original takes place almost entirely in Andy's house, with a little bit over at Sid's house (although yes, that's a very important part).
Toy Story 2 takes us out into the world. Pizza Planet, the airport, the chicken man's place, etc. We find out that Woody isn't just some generic cowboy figure, but part of a much larger world as well, and that world is explored. To me, it's definitely not a "more of the same" sequel, but a "let's take things further" sequel. And then
Toy Story 3 is pretty much the perfect ending to the trilogy. It takes things even further, actually gets kinda dark and scary, but also is completely faithful to the original and has numerous callbacks to it. And of course it provides closure to the original story while at the same time assuring the viewer that things will continue.