Putting elements of all this together, if you take two telescopes with the same aperture, one f/5 and one f/10, then the image will reach the same "brightness" (accumulation of photons resulting in electrical signal on the sensor) 4x faster with the f/5 scope than the f/10 scope.
Of course, if you're using the same sensor in this example, your resolution (per pixel) will also be 1/2 in each dimension, i.e. each pixel is seeing 4x the amount of sky as when attached to the f/10 scope...
Depending on your target, there are pros and cons to each
