Scopes themselves are not faster or slower.
Gathering a certain amount of light over a given area can take less time (faster) or more time (slower).
If we can gather that amount of light faster (in less time), then we call the equipment that gathered that lighter "Faster." Now, in this sense, we can call one scope faster than another.
The amount of light you can gather is determined by the overall aperture of the prime optic. Let's say light is water. In one minute you can get one "bucket" of light (water) through the aperture, say.
Now, empty that bucket into a pan that is 12 inches by 12 inches, you will get, say 3 inches deep water.
Empty that bucket into a pan that is 8x8 inches, you will get almost seven inches of water.
Have you gathered more light? No
Have you gathered it faster? No. The speed at which you can gather light is fixed by the aperture of the Prime Optic.
Have you gathered more in the given area of interest (in our case---is there more depth to the water in the one pan than the other)? YES. You did not gather any more light (water), but the intensity of the light (depth of the water) is greater. It was faster.
Changing from from F10 to F6.3 reduces the size of your pan. All the light that used to spread over X area, now spreads over the smaller .63 * X area. And each part of that smaller area has more light, more water, is faster.
Of course, the distance from one part of the scene to the other has also been reduced. Instead of covering the area that was covered at F10, it has to be rearranged into the area covered by F6.3. So, things are smaller (not as magnified).
The primary optic has not changed. It is still gathering as much light as it had been. And it is converging the light at a rate of 1 to 10. It is a light cone ten times longer than it is wide. But, someplace along the way, you will stick in a focal reducer that will change the angle of the sides of that cone so that it is only 6.3 times as long as it is wide. This brings the sides of that cone together sooner, and into a smaller area. Because the same amount of light is hitting a smaller area, any given part of that area will see more of the original light. It will reach a given exposure point more quickly. It will be "faster."
The scope will now have a final light cone, and an APPARENT focal length of a scope with a F6.3 focal ratio. You will gather your images (get them to a given exposure level, depth of the water, etc. ) FASTER>