Jack Russel Terriers are used as hunting dogs. They are fast and small, so they can get into little crevices and holes. They chase down little animals like mice, rabbits, gophers, moles, etc. They are mean and have sharp teeth.
There is only one breed of JRT. If someone is advertising a "miniature," they are simply using a jimick to try and charge more for out-of-standard dogs. For example, if I had a litter of German...
The Jack Russell Terrier is a dog breed that might be best described as a small working terrier. It could be argued that the standard is still being defined, but one could use the link and read more.