How did the views of the Whigs and Democrats differ from those in the Free-Soil Party?

The Democratic Party, a linear descendant of Jefferson's Democratic Republicans but with less fully articulated views, was formed mainly with the purpose of electing Andrew Jackson as President. It was, for most of the 19th Century, the party of Southern planters, slaveholders, and the interests of Southern whites. Its durability in American politics owes more to its flexible adaptive qualities than to its enduring principles.

The Whig Party was founded in 1833 by Daniel Webster and Henry Clay, explicitly as a rejection of Jackson's presidency. "Whig" means "anti-tyrant" and the tyrant in question was Andrew Jackson.

Today we dislike Jackson for his views on slavery and the Indians, but the Whigs' detestation was rooted more in class snobbery (Jackson did not come from the same social class as his six predecessors, although he was an active participant in the Revolution and the breakout star of the War of 1812, and his wife was involved in a bigamy scandal that would scarcely make the Twitter feeds today).

The Whigs fielded three presidents, one of whom assumed office on the death of another and was promptly kicked out of the Party. Anyway, they disbanded in 1854.

The Free Soil Party was the party of Northern abolitionists. They opposed slavery on moral grounds, but acknowledged that the Constitution permitted it. Mainly, they wanted to keep slavery from expanding into the Southwestern territories gained during the Mexican War. the party was formed in 1848, fielded no successful presidential candidates, had little popular appeal outside Boston, New York City and Chicago, and was folded (with the Whigs) into the Republican party in 1854.