You know how a square is a rectangle but a rectangle isn't a square?
The terms "free climbing" and "free soloing" are the same way. Like this:
"Free climbing" just means that you're using your hands and feet to rock climb. It's the opposite of "aid climbing", where you directly use the rope and gear to climb (by physically standing on it/pulling on it--yes it is weird), as opposed to it only being there to catch you if you fall.
"Free soloing" is just a version of free climbing where the climber is not using any gear, like a rope, to protect themselves if they were to fall.
So, free soloing is free climbing, but free climbing is not free soloing.