Jefferson created the political party to oppose the economic and foreign policies of the Federalists, a party created a year or so earlier by Treasury Secretary Alexander Hamilton. The republican party opposed the Jay Treaty of 1794 with Britain (then at war with France) and supported good relations with France before 1801. The party insisted on a strict construction of the Constitution, and denounced many of Hamilton's proposals (especially the national bank) as unconstitutional. The party favored states' rights and the primacy of the yeoman farmer over bankers, industrialists, merchants, and other monied interests. There was always a range of opinion within the party on issues of commerce, public works, and industrialization, which were more warmly received by Madison and the Democrats than by Jefferson and the Republicans; but this was a preference, not a firm ideology on either side. Jefferson signed a bill funding a canal for the Potomac in 1805; Madison ended his term in office vetoing a public works bill.
Jeffersonian purists, or "Old Republican" wing of the party, led by Jefferson, John Randolph of Roanoke, William H. Crawford, and Nathaniel Macon, favored low tariffs, states' rights, strict construction of the Constitution, and reduced spending. It opposed a standing army. The "National Republicans," led by Henry Clay, John Quincy Adams and John C. Calhoun, eventually favored higher tariffs, a stronger national defense, and "internal improvements" (public works projects).
After the Federalist Party broke up in 1815, many former members joined the nationalist faction of the party.
In order to be able to make a difference between Jefferson's republican party and the Republican Party of our days, some have begun to retro-actively apply the name Democratic-Republicans to the party formed by Thomas Jefferson and James Madison around 1792.
However, they and their supporters identified themselves as republicans. In the political climate of Jefferson's day, "democrat" was actually considered a pejorative.
So, while the term "Democratic Republican" was also used by contemporaries, it was used mostly by the party's opponents.
If you want some more information, take a look at this chronology
http://www.access.gpo.gov/congress/senate/repub_policy/pdf/03Chro.pdf
