Yes you certainly can get different sounds from each channel, the degree to which they differ depends on the recording technique and the preferences of the sound engineer involved. Some Beatles recordings for instance have the main vocals on one "channel" only.

Stereo sound is produced either by recording a live performance with dual microphones, one for each speaker; or by mixing individual sources in post-production to create a stereo image. The signal for each speaker is then encoded into a channel on the storage medium. For example the Red book audio specification for CDs mandates two channels for audio recordings. During playback the CD player will decode the audio for each channel and route it to the corresponding speaker.