Did the federalist and anti federalist give birth to the democrats and republicans?
No. The Democrats were formed around 1796 as the Democratic-Republicans. Thomas Jefferson was the first President to be a member of this party, as John Adams had been a Federalist. (Technically Washington had no formal party that he was a member of.) Over time, this Democratic-Republican party became known as simply the Democratic Party. The Republican Party did not arrive in American politics until the 1850s. They arose from the ashes of the recently-defunct Whig Party. Abraham Lincoln is commonly referred to as the first Republican President, although he was never formally a member of the Republicans. During his first campaign, he was a member of the Unionist Party and only began calling himself a Republican after his second election in 1864.
