Is there a difference between free climbing and free-soloing?
Yes, it's a big difference.
Free climbing contrasts with aid climbing wherein the climber uses gear on the wall and various slings and stirrups to make progress upwards.
To climb free is to only use your hands and feet to hold yourself and move over the rock face.
And free soloing is to do this without a rope or anything else to catch you if you fall. The consequence of a mistake is death.
Laypeople—the popular press in particular—often use the phrase "free climbing" when they mean "free soloing". It drives us nuts.