Things that are miniature are teeny tiny versions of something else. Think miniature poodle. Unless you don't like small dogs. Then think miniature footballs. Aww, cute.
When something is a miniature, it is like it has been shrunk down in size. It's not just small, it's a small replica of something else. If you made a dollhouse that was a scale representation of your own house, it would be a miniature of your home. It would also be a little weird.