Actually the shift in ideology and thus the split in the Democratic party started in the mid 1940s with FDR. The first major split of Southern Democrats was in the 1948 Presidential election when Southern Democrats split and ran Strom Thurmond as the "Dixiecrat" candidate. By 1964 the shift was long since over.
The Republican Party has always been the party of business. The change there occured when Southern Democrats joined and pulled it the right on social issues. That change occured during the 60s and 70s, Reagan reinvigorated the already conservative Republican Party. Reagan, though, wasn't really a hard-core social conservative. Barry Goldwater was the first real hard-core conservative Republican to run for President.
How do you tell the two apart on the street? Easy, the Democrat is volunteering to help clean the street, while the Republican bitches about having to pay for it.
acludem