Are there different kind of Miniature horses?

Fact: No

There are only Miniature horses. But breeders like to pretend there are sup-classes such as: micro mini, arab mini, draft, Quarter horses style, act. Since all breeds were taken to make the Miniature horses some will look more like a larger breed than others. In the showing world the arab style is more popular. Some people have come up with Micro minis which are nothing more than a Mini horses that is 30" or under. 

Now there is the dwarf mini horse. But saying they are a different kind of breed rather than just a mini would be like saying little people are different from tall people. The Dwarf mini horse is only a mini horse that inherited the dwarf gene from both parents, which is stronger in some bloodlines than others.

So people have come up with sub category names but its all by chance. You can have a 32" mare and 32" stallion and get a baby that gets 29"as a adult. You can have 2 horses that look nothing like an arab and get a baby that dose.