have you ever seen Brad on top rope?
he sucks!
for him, leading is climbing, and he has a good lead head about him.
The more common miscommunication I think is the
"I've done x" Where x = a climb.
To say you've done x, but not clarify whether you've fallen on it, or followed it is misleading.
Absolutely, if you climb it whether falling on it or not, you've climbed it, unless of course you pulled on gear to make upward progress.
I usually stick to either "I've done x" or "I've been on x" but usually even the later is followed quickly with a style notation.
I can't think of a time when I wouldn't have used these or similar denotations. I used to get mad at people for talking as if they had lead it, e.g by describing someone else's lead efforts, and then saying that they had 'done the route.' or earlier saying they had 'done the route' No I just feel sorry for them that they need to have a false ego like that.