Hmm, it works fine here, dragging two different songs (from the desktop) into two different tracks -- I can play either or both. Note -- I'm assuming by "songs" you mean audio recordings, not MIDI files, and you're trying to add them to Audio tracks, not Instrument tracks..
What exactly do you mean "the first becomes the exact same song"? You may need to supply a little more detail about exactly what you're trying to do, how you've created the tracks, and how you're bringing the songs into GarageBand, along with the basic specs of your system (GB version, OS version, audio file types, etc)..
Off the top of my head, maybe you've accidentally created two tracks that are not fully independent (this is possible in Logic, though I don't know if it's possible in Garageband). If this is an exiting Project, you might want to restart the computer, re-open GB, create a new empty Project from scratch, create two tracks, and drag in each song to its own track, to see if it may just be a gremlin that goes away after a fresh start..
