Good Brian. Now I can see better what you need to know.
As stated above, the only factor that makes a lens "Fast" i.e. able to gather more light, is the diameter of its outer lens in relation to its focal length. This is technically expressed as "F" number. The smaller the F number, the faster, the wider (Its lens diameter and not image it produce)is and for eg F 1.4 is 5 time stronger to gather light as opposed to F 5.6 with steps being 1.4 > 2 > 2.8 > 4 > 5.6
So if you need a lens to gather more light, be useful for indoor or night, you need a Large aperture or small F number (Reverse relation). Be aware the prices go logarithmically high as aperture becomes wider.
Wide Lens is a lens that takes large field of view image or in other word a Wide angle. Typically for a 35mm classic film camera or in digital life, a “Full Frame” camera, a lens that has focal length of 35 mm or lower and when you get to 17mm or lower you are talking of Ultra Wide lens, when getting to 8mm or lower, you are talking of Fish eye. For cropped sensor DSLR, use the crop factor to find the exact equivalent focal length by dividing these numbers by crop factor. This has nothing to do with light gathering and all can be equal in that respect say if all have F4 aperture as the largest.
As for real stuff i.e. Macro, I though this might be of use for others too who have never tried macro so started another thread.
Here Is the L I N K.
Enjoy reading and hope this is useful to you.