There are indeed specialized subgroups within druidism. Although some of them are very, very easy to attach to one of the in-game druid specializations, not all of them are.
Druid subgroups differ, lorewise, by their chosen patrons. For example, a Druid of the Talon follows the teachings of Aviana, the Mistress of Birds. A Druid of the Claw follows Ursoc and Ursol (as you rightfully pointed out!) but not Ashamane – that would be the Ashen, protectors of the Fangs of Ashamane and followers of Ashamane’s teachings. There are also Druids of the Branch, who (presumably) follow the teachings of Aessina. But since this isn’t really your question, I won’t ramble about this.
First, the Druids of the Talon. They are Druids who chose Aviana as their patron, and it shows in that they take the form of birds. But it is very hard to slot the Talons into an in-game specialization; the bird form is a general ability usable for all specializations. With what little overlap they have, I’ll probably say Balance is your best bet – but in general, all work for Druids of the Talon.
Druids of the Wild are a tricky one, because these are Druids that follow all paths; they learn all forms, they learn all kinds of magic, and are essentially jack-of-all-trades. They do not lock themselves to one Wild God. Generally, the PC Druid is considered a Druid of the Wild, considering they have mastery over all forms and are able to pick whatever specialization they want in-game. So, any specialization!
We know very, very little about Druids of the Moon. However, the namesake of the Druid subgroups often refers to what they do or who they follow (e.g Antler = stags = Malorne, Talon = birds = Aviana). We see, however, that Druids of the Moon shapeshift into Moonkin and that means they, combined with their name, makes them a very, very likely participant for the Balance specialization.
Druids of the Grove are much like Druids of the Moon in that we know fairly little (even less than the Moon druids, actually). I don’t think they have any particular specialization that they can really be assigned to, considering they are very vague. In-game, they often simply seem bound to one place/one “Grove” that they protect (see: Alterac Valley). As such, it’s nigh impossible to place them into a specialization because we simply know too little about their capacities.
A little correction here: although Druids of the Claw were showed as being able to use Cat form in the past (and they probably are!), they do not follow Ashamane as their patron. That would be the Ashen, protectors of the Fangs of Ashamane who consider the Panther to be their patron.
I hope this was clear enough. The post became a lot longer than I wanted it to be - let me know if you have questions!