No, the Sheltie is not a 'Miniature Collie,' even though it looks like a diminutive version of the Collie. Because Collies and Shelties share some ancestry, they do bear a resemblance to one another, and early versions of the Shetland Sheepdog were crossbred with Collies to refine them. But Shelties and Collies—two distinct breeds—developed independently of one another.
There is no such thing as a 'Miniature Sheltie,' and if a breeder claims to have them, they're merely breeding undersized Shelties to achieve a smaller dog. The AKC maintains standards for only one recognized breed, and that is the Shetland Sheepdog. If you want a smaller version of the dog, your best bet is to seek out a reputable breeder and choose the smallest pup in the litter.