Answer:
Short answer: Not quite. Calculus AB covers more (and goes more in-depth) than Calculus 1.
Long answer:
The AP Calculus AB test covers differentiation (taking derivatives) and integration (taking antiderivatives). In college, Calculus 1 mostly covers only differentiation and Calculus 2 covers integration and series.
I like to think of it like this:
A = Differentiation
B = Integration
C = Series
So Calculus AB covers differentiation and integration and Calculus BC covers integration and series.
College is more like:
Calc 1 = A
Calc 2 = B&C