Hi Mark,
Yes - it all gets very confusing very quickly once you start getting into the technical details of focal ratio, SNR, Airy disks, resolution, point-spread functions and Gaussian profiles.
I think the simple answer to your question is this - the only thing that matters with respect to light-gathering power is the diameter (and hence the area) of the aperture.
The f-ratio (or the focal length) simply determines the area over which the light gathered through the aperture is spread when it arrives at the image sensor.
So, light gathered by a 50mm telescope is spread over a very small area on the sensor, and hence is very bright. The same amount of light gathered by a telescope with the same aperture but a longer focal length is delivered to a much larger area on the sensor, and hence is less bright - so requires a longer exposure - all else being equal.
It is a function of the areas - which is why standard f-stops increment by a factor of √2.
Telescopes are just big cameras - so the same principles apply.
I hope that helps
Gary