Actually one still is. The Democratic-Republican party dropped the Republican from their name. They are running Obama in 2012.
I would not say that. The Democratic party may indeed have its roots in the Democratic-Republican party, but I wouldn't go so far to say they are the same party, the simple fact remains that a D-R candidate from yesteryear would not fit at all in the Democratic party today.
Some people would agree and point out that the co-opting occurred about the same time they took the word 'liberal'. That group has shown itself as skilled at camouflage as a chameleon.