There are really two different types of bicycle saddle bags. Firstly there is the traditional large bag that fits to the rear of the seat, has a large compartment and possibly side pockets. Secondly there is the smaller seat bag or seat pack, which fits under the saddle either to the saddle or to the seat post.
Many people who cycle for leisure at the weekends prefer the traditional saddlebag as it can carry quite a lot of stuff but doesn’t necessarily need to have a rack fitted to the bike. There are not many manufacturers of traditional saddle bags these days , the main one in the UK is Carradice.
The seat bag on the other hand is useful to those who want to carry the minimum on their bicycle, i.e. nothing other than tools and a fruit bar. It is also useful to cycle tourers as an additional place for storing small items that may be needed in a hurry. Many seat bags come with a special fitting so they can be attached to the seat post.