In this litter of six puppies, three were Wire Haired and three were Smooth or Short Haired. As the American Kennel Club lists all Dachshunds as one breed with 6 "Varieties" and in the United States those 6 varieties can be interbred. So a Standard Long Haired Dachshund "could be" bred to a Miniature Wire Haired Dachshund. Most breeders do not cross coat or size unless there is something specific they are looking to add to their breeding program. In the development of the miniatures, it was not uncommon to use a small Standard bred to a Mini to bring in some of the attributes of forechest, keel, length of ribbing, coat texture or other factors to the smaller dog who could be lacking in some areas.
Still today mini smooths will be crossed with mini wires to perhaps bring better coat texture to the wire or a more outgoing personality to the smooth. We in Canada can produce smooths in a Wire to Wire breeding and the resulting smooths are registered with the Canadian Kennel Club as a Smooth from a "recessive" gene. If you see the letters of MW at the end of our dogs names that is an indication of it being a Mini Wire. If you see a MS that is a Mini Smooth. Because the American Kennel Club simply refers on the registration that they are a "dachshund" most breeders when registering the puppies will indicate which variety so when looking at pedigrees you will know what is involved behind a dogs genetics.