On a simple level, I remember,
- Pre-algebra: linear equations in one variable, 7x +10 = 5-3x
- first year HS algebra: lots of lines, y=mx+b
- second year HS algebra: conic sections, exponents, logs
The manipulation work in pre-algebra to sort out and solve for the x, is a basic skill that is called on in many higher classes. Often re-arranging the spinach, to see clearly enough to apply some rule, is half the battle.
We had a heavy dose of inequality battling in a course called "functions", which along with analytic geometry came after Algebra 2, and served as pre-calc. I disagree with Robbie's comment about inequalities in the context of pre-algebra. That topic should come later.
[EDIT] Note that some elements of algebra are included in pre-algebra. Just as some derivatives and anti-derivatives are included in pre-calculus ("functions" and analytic geometry). Well...at least in Fairfax County public schools of the 70s and 80s. And Algebra 2 covered all the logs and such that are part of "college algebra". And there was a full semester on trig also (after algebra 2), but before "functions". The GT kids took Algebra 2/Trig (which was 3 semesters in 2).
But I would not rely too much on names. Looking at textbooks, I see several pre-algebra texts that have the "solve for x" as key content. It's like baby steps into algebra. Then they throw a y in along with it in algebra 1.
For example this is the first hit on google (that I got for a prealgebra textbook pdf).
Note that they get right into solving for x in chapter 2 of the book. (See page 91 for the classic adding things to both sides of the equation stuff.) Granted, there's a bunch of pictures of girls with horses...don't rememember that when I did it. But "solve for x". Classic pre-algebra. Kid has exercised that before high school algebra 1.