Maybe I am misunderstanding, and someone can set the record straight for me. But from what I understand, around the time James Monroe became president, the Federalists collapsed and ceased to exist, and there was only one party for the remainder of his presidency, the Democratic-Republicans. And then at the end of his presidency, the Democratic-Republicans fractured into multiple parties.
So wouldn't that make John Quincy Adams and his allies Democratic-Republicans? But then when that party fractured, it just so happened Adams aligned himself with the pro-centralized government faction that became "National Republicans" and later "Whigs"? Or is there some nuance I'm missing? What was it that distinguished the Federalists from the National Republicans/Whigs? And what distinguished the Jeffersonian Democratic-Republicans from the Democratic Party of Andrew Jackson and Martin Van Buren? Why aren't they both considered continuations of the earlier parties?
The National Republican party (which eventually became the leading block of the Whig Party) and the Democrat party were both offshoots from Jefferson's Republican party. By the early 19th century there were multiple factions within the Republican party, Nationalists like Henry Clay supported tariffs, internal improvements, a stronger navy and army among other proposals that James Madison embraced late in his presidency. It may Surprise you to learn that one of the leaders of the nationalists was none other than John C. Calhoun who at the time spoke quite eloquently in promoting the national agenda, he'd only become an ardent sectionalist later on
" Let us bind the republic together with a perfect system of roads and canals. Let us conquer space
Then there were others in the Republican party who were more distrustful of a strong national government, men like John Randolph formed a group called the quids which often found themselves opposed to Clay and others.
The Missouri crisis in 1819 was a rude awakening for many, and without two strong national parties the fear was divisions would fall on sectional lines (which did indeed happen in 1860). A Republican, Martin Van Buren recognized this and worked furiously to restore the two party system usually at the expense of John Quincy Adams administration. He stated
party attachment in former times furnished a complete antidote for sectional prejudices"
As far as Federalists. They had become somewhat of pariahs nationally after the war of 1812. During the war they often hindered the government's war efforts, refusing to call out militia, hindering recruitment and even going so far as to correspond with British military officers. Republicans often referred to them as Blue Light Federalists, a term in reference to showing British naval ships a blue light as a warning. Most importantly they had held a convention at Hartford in late 1814 which was interpreted as hostile to the nation. Unfortunately for them news of their convention came out right as news of Jackson's victory in New Orleans and subsequent end of the war.Thus the Federalist legacy was not really embraced by either party.
Federalists would of course eventually filter into the two new parties, Daniel Webster for the Whigs and and Roger Taney for the Democrats were two former federalists who worked their ways into prominent roles for their respective parties eventually. But the stain of the Hartford convention would last a long time