Question about the new songs (DLC)

A few years ago I bought GTA 4 along with the dlcs on Xbox, so it's not the disc. I'm now playing TLAD but have yet to hear any new songs. I played TLAD last many, many years ago but I could swear there was new music on it back then.

I googled it, but honestly it's all a bit confusing for me. Do I understand correctly that if I have the DLC (digital) I don't have new radio stations but the new songs should be included on the existing IV radio stations?