"wear" and "put on"

[David Palfreyman]

My non-native English-speaking brother-in-law and his native
English-speaking wife were preparing to go out, and running late.  He
indicated a dress and said "wear that".  She said "OK" and went on doing
her make-up.  A minute later he said in frustration "come on, wear
that!"  It turned out that he meant "put that on".

Now, I can see the difference in meaning between the two verbs, but how
would you describe it in semantic terms, and are there other pairs of
verbs with a similar distinction?

:-D