Anterior shin splints are really the only kind of shin splint. Usually caused by muscle imbalance and/or weak tibialis anterior muscles. There are stretching and strengthening exercises you can try.

Medial tibial pain is very common, and usually, incorrectly, called shin splints (got its name back when no one had a clue what was really happening to cause the pain). If you think this is actually what's going on, do a google search for sports med articles relating to "medial tibial stress syndrome".