When I was growing up, Republicans stood for individual and states' rights (especially in the white South), Democrats stood for expanding rights to African Americans (especially in the white South). The first Republicans came in to being in 1860 to fight black slavery. The Republicans of the mid-twentieth century stood against black equal rights. Mid-twentieth-century American politics was the second fighting of the Civil War; only the parties had switched sides.
Then the Republicans stood for a smaller Federal government, one that would not tax Americans to death. While the Democrats were paying for every conceivable social program they could think of.
Neither Democrat nor Republican has seemed to have much trouble committing us to war; although we can certainly quibble over what wars we should have gotten involved in.
The Democratic president who seems to stand for what it means to be a Democrat was Kennedy-Johnson, Kennedy's youth, passion and compassion and Johnson's driving the Congress to do his (Kennedy-Johnson's) will: creating the Great Society.
The Republican president who seems to embody Republicanism was Reagan. The Reagan of get tough with the Communists (who were falling apart due to internal problems) and of Star-Wars and of trickle-down economics. But Reagan was not what he seemed: he was charming as the day is long, he gave Conservatism a good name but he spent more than any Liberal Democrat ever imagined and more than doubled the National Debt in his eight years. He was not a fiscally-responsible Conservative!
But the real differences between the Republicans and the Democrats in the past 50 some years has been their constituency. Republicans have been funded by big corporations and have been backed by big money and the Bible Belt (Reagan was only one president to claim to be Born-Again). Democrats were the party of the poor and the middle-class. Until the middle-class all but vanished and the Democrats began to be funded by big business too. The Democrats in the past 20-30 years have become proto-Republicans.
In other words, every politician is beholden to Big Business and to ignorant voters.
It is a sorry state.