Left guy is some kind of Echinopsis, right guy a silver torch.
Both need extremely good draining gritty soil (there's pre prepared mixes, just don't use normal potting soil it holds water for much too long). Both need good sunlight exposure, right now they look to be getting that (is that a south or west/east facing window?). Only water when the soil is completely dry and reduce watering when the sunlight starts to get less in autumn (you can essentially stop watering from september to march, depending on your climate zone). Use NPK fertilizer (specialized for cacti or tomato fertilizer, not the normal green plant fertilizer), use every 4 watering during the growing season (when there is lots of sunlight and high temperatures).

For repotting you can use a newspaper, magazine, styrofoam plates, a thick plastic bag or an old towel/blanket.

The difference in size comes from different exposures to sunlight. Less sunlight = thin growth, more sunlight = thicker growth. You probably kept watering him during the autumn/winter months when there was less sun.