Silvan/Sindarin/Avari....

[Legolas]

The way I see it, 'Silvan' is a more general term that was taken on by elves in later days.

The Sindar, they were called, who stopped near the coast and took Thingol as king; the Nandor, who followed Lenwe down the Anduin; a few of the Avari, that did not start the journey at all, and a few may have found their way into the region; any of the Noldor that hadn't returned to Valinor - a good number of all of these faded into the Silvan melting pot.

I'd imagine the Silvan elves started out as mainly Nandorin, as The Silmarillion defines them. As time went on and so many of the elves took the regions immediately eat of the Misty Mountains, the kindreds that were so strictly separated in the First Age were mixed together so much that the new elves being born were not easily distinguished as being more of one kindred and less another.

Of course, not all of them would be all mixed up - especially leaders and those from from the earlier ages and their direct descendents (i.e. Thranduil, Celeborn, Galadriel, and Legolas, though he calls himself Silvan and is so by culture, he's obviously Sindarin by heritage).