Chris, because of the time constraint my answer will have to be relatively short, but I'll try to do my best. The AKC standard for the breed gives a good description of the wirehaired coat:
"With the exception of jaw, eyebrows, and ears, the whole body is covered with a uniform tight, short, thick, rough, hard, outer coat but with finer, somewhat softer, shorter hairs (undercoat) everywhere distributed between the coarser hairs. The absence of an undercoat is a fault. The distinctive facial furnishings include a beard and eyebrows. On the ears the hair is shorter than on the body, almost smooth. The general arrangement of the hair is such that the wirehaired Dachshund, when viewed from a distance, resembles the smooth. Any sort of soft hair in the outercoat, wherever found on the body, especially on the top of the head, is a fault. The same is true of long, curly, or wavy hair, or hair that sticks out irregularly in all directions. Tail-Robust, thickly haired, gradually tapering to a point. A flag tail is a fault."
The FCI dachshund standard (description of the ideal) states: With exception of muzzle, eyebrows and ears, perfectly even close fitting, dense wiry topcoat with undercoat. The muzzle has a clearly defined beard. Eyebrows are bushy. On the ears, the coat is shorter than on the body, almost smooth. Faults include:
• Soft coat, whether long or short.
• Long coat, standing away from body in all directions.
• Curly or wavy coat.
• Soft coat on head.
• Flag on tail.
• Lack of beard.
• Lack of undercoat.
• Short coat.
Joeri would be a good example of ideal wirehaired coat - a nice bushy beard, yet tight wiry, harsh body coat, no hair on his ears. Wirehaired dachshunds need to be groomed, and Joeri is not an exception. This will be a topic for another post, but I just would like to mention that Joeri looks good when his coat is stripped 2-3 times a year.
Ideal wirehaired coats do not breed true, and this is a big problem when it comes to breeding wirehaired dachshunds for the field. Even when both parents have ideal coats, most likely their pups will have a whole range of coats. Those who have been following this blog, probably remember that Joeri and Emma's four pups included smooth Olive, Ollie with a very good coat, and Olana and Oak with softer coats.
When it comes to hunting dachshunds, who do you think will have a more functional coat - Bernie or Angie?
Above - Bernie came out of parents with ideal coats. He has a double coat typical for wires (true smooth dachshunds have a one-layer-coat), but his topcoat is very short, and he does not have a beard, eyebrows or leg furnishings. Technically he is a smooth dachshund.
Angie has a soft and fluffy coat, which has not been groomed. If she went like this into a thick cover, her coat would be a complete mess. If she were to be used for field work, her coat would have to be clipped and kept very short.
Both Bernie and Angie have faulty coats, but Bernie's coat is much more functional than Angie's. His coat is double layered and provides good protection; there is no grooming required. Angie's coat does not provide protection and would be a liability in the field. However, some people love the look of wirehaired dachshund with a beard, and would choose Angie over Bernie, if they were basing their decision exclusively on the coat type.
Different registries and breed clubs treat the smooth coat coming out of wires differently. In the USA there is only one breed - the dachshund - and a registration certificate does not even state the coat type. If Bernie were to go to a show ring - he would be shown as a smooth dachshund. In the FCI countries, where crossing various coats of dachshunds is forbidden, individuals like Bernie are disqualified from breeding. In other countries, like Canada, he would be re-registered as a smooth. The problem of smooth and soft coats does not exist only in wirehaired dachshunds but it is encountered in other wirehaired breeds such as Deutsch Drahthaar or Wirehaired Pointing Griffon. A good discussion of problems with coats in the latter breed is at http://www.griffonpoint.com/wire-coat.htm
In Germany, since smooths out of wires are penalized and disqualified from breeding, many breeders try to avoid them and tend to breed softer, fuller coats that are not very functional in the field. By the way, "smires" is just a made up term used by enthusiasts of this type of coat.