Climbing pedant checking in. I think the type of climbing you're referring to is free-solo, that is climbing alone with no partner or protection from falling. "Free climbing" is climbing using only hands and feet for upward progression but typically involves the use of protection (gear, ropes, and a partner) to save you in the event of a fall. It's called "free" because the climber does not use metal tools, hooks, pitons, or bolts for upward progression like in aid, ice, or alpine climbing.