Note: I am not an American, have never lived in America, so apologies if this is something that a US school kid would know.
There have been shifts in the party system over time, which are not exactly neat or clean, but you are correct that around the time of the American Civil War, when the Republican party was founded, it was generally speaking the left-leaning or liberal party (the abolition of slavery being pushed by Republicans) and the Democrats were the more conservative party. The shifts over time are detailed pretty well in our FAQ.