From what I've been learning recently (mainly in this great forum, I must say), the amount of light depends on the aperture, period. Same aperture, same light gathering ability.
The issue here is related to AP when trying to obtain the same picture with different telescopes.
We should obtain the same field of view with telescopes that have the same focal length, let's say for example, 1500 mm.
These very same 1500 mm could be obtained with a 300 mm aperture telescope, an f/5, or with a 150 mm aperture one, an f/10.
The first one gathers 4 times the light of the second one (4 times the area), so for the very same picture the f/5 telescope requires 1/4 the exposition time of the f/10 one, hence one is named "fast" and the other one "slow".