Computer glasses are not the same as reading glasses. I don't know if you have progressive or bifocal/trifocal lenses, but the idea is that glasses are usually a compromise, optimized for a particular viewing distance. Bifocals and trifocals have two/three sections of the lens, each optimized for a different distance (near/far).
Progressive lenses have continuously variable "sweet spots", the top of the lens is best for distance viewing, the bottom for close-up, and varying in between. However, in standard progressive lenses, the sweet spot for 18-24", the typical monitor viewing distance, is very narrow. Computer glasses have a very wide/tall sweet spot optimized for computer viewing - they're not very good at distance and may not be good for reading. (I do best reading without glasses.)
If you have single-vision lenses, then I guess computer glasses would also be single-vision, but optimized for computer viewing distance. Ask your eye doctor.