What are the different types of veneers?

Multiple. Main ones are porcelain or composite veneers.
Not very many... We only do porcelain veneers in our office but there is also the option of a lumineer. Lumineers are similar in cost but are just like putting a fake fingernail on your tooth. They can be removed later down the road. If you are going to spend the money to do a veneer i would suggest doing porcelain veneers which is the highest quality.
Another option. There are the traditional prep veneers where the tooth is shaved down about .5 mm for either porcelain or composite veneers. A second option is also known as a no prep or very slightly prepped veneer (lumineers). This is popular because of lack of grinding or limited grinding of natural tooth structure compared to the traditional veneers. Each case is unique and needs to be evaluated.
Six different kinds. 1. Porcelain and composite. 2. No prep and prep. 3. Direct indirect. Your cosmetic dentist can help you decide which procedure or combination of procedures is right for your individual case.
Direct vs indirect. Direct veneers or bondings are composite laminates. The indirect veneers are porcelain veneers requiring more than one appointment. Different material and procedures used for porcelain veneers like prep vs no prep porcelain veneer also divide it into other categories.
Porcelain, resin. Most veneers today are porcelain. These can be placed over the tooth like a fake fingernail but not ideal due to adding extra to tooth. Also you can do a porcelain veneer with very slight tooth reduction probably more ideal. There are probably these same options with a resin material less expense but less quality and duration is a problem. Tooth colored filling material can be painted on.