Stereo records contain left-right information on each side of the groove-walls. The walls are angled at 45 degrees from vertical. Both horizontal and vertical information is presented to the cartridge generator.
Stylus movement when playing a mono record is side to side (horizontal) with no vertical movement. Mono catridges are designed to trace the horizontal movement only. A mono designed cartridge will help with the noise floor and present a better detailed representation of the mono recording. The results is amazing.
Stylus size for the widest use (old 1950 and new 1960) is .7 mil, which is my preference. If only 1950 era recordings are played you may use a 1 mil.
If you have many mono records, a Miyajima mono cartridge is the best I have found for reproduction. Ortofon has a excellent entery level cartridge.
Ortofon has an excellent explanation of record grooves at: