> The names of the parties Republican & Democrat aren't just random words, they represent the philosophical differences in where the bulk of the power in government should rest
No, they don't. Also, the two original parties were the Democratic-Republican Party of Jefferson, Madison, et al., and the Federalist Party of Hamilton, Adams, etc al.
Both, BTW, favored what is, I modern terms, a democratic republic and a representative democracy, though the Federalists initially favored a stronger central seat of power and the Democratic-Republicans favored a weaker central seat of power, though the bigger divide quickly became over foreign policy.
The Republicans weren't a major party until after the Federalist Party collapsed leaving a brief period of unstable one-party domination, then the D-Rs fractured, leaving the Democrats and Whigs in the Second Party system, then the Whigs later collapsed and the Republicans and the Democrats formed the Third Party system with the most critical initial issue being over not abstract form of government but slavery. While the identity of the two major parties has been the same since, their political alignment has changed several times; we’re now in what is generally regarded as the Sixth Party system.