What is the difference between miniature and standard brushes?
"Miniature" is a reference to the length of the tuft of bristles from end of the ferrule to the tip of the brush. 

There is no standard to how measurements for artist's brushes are shown. The measurement is usually a number stamped on the side of the brush handle. A company standardize their own number system but that doesn't necessarily mean it's the same number system as compared to another company's number system.

The handles too are not standardize to length size either. The handle can be any length for standard or miniature ... but in a company's own series of brushes the length of handle, ferrule and tuft decreases as you progress in size from standard to miniature.

It's things like this nonstandardization why artists spend a lot of time and money experiementing with different equipment and manufacturers to find the best tools that work for them.