Is it possible to play one song through speakers, and another through headphones/earbuds?
You can use a piece of hardware called a MIXER to take two (or more) audio signals, mix them together, and have one OR MORE outputs.  For example: Behringer XENYX Q502USB / Audio interface.  

There is a learning curve for operating a mixer (where to plug in the sound source / what cables to use), but if you want to take recording to the next level, you might enjoy getting a mixer.