Baggy shorts sometimes come with a padded insert, which is invariably sized differently to the short itself. I've never bought tight cycling trews that didn't have an insert, although I believe they do exist.
afaik, you buy stuff either with or without, you don't really want the pad to move around so it's stitched in, they're made of something that's supposed to be hygienic and you're supposed to wash them anyway
if you're doing any sort of miles think hard about some bib longs, I've only recently stepped up to them and they're really excellent on so many fronts
wiggle do a tip top pair for the princely sum of £18
you can buy either padded shorts (which you go commando) or padded undershorts (to be worn with non padded cycleshorts/baggies). the trick is not to wear them together as too much padding has the opposite effect of what it's supposed to do.
padded cycleshorts/longs whether bib style or not, often come with a proper chamois whereas undershorts tend to have foam padding. the chamois is more comfortable.