atan is the same thing as the inverse tan.
the "arc tangent" terminology comes from geometry: what is the arc (angle) that produces a given ratio.
(for a unit circle, the length of the arc is equal to the angle)
atan2 is a better atan that handles divide by 0 and also knows which quadrant we're in by taking in the projections instead of the ratio.
tldr - atan2(y, x) for when we need to know the angle cast by a vector projections y and x