A briar patch.
A patch of clouds.
Word: "patch"
different meanings

He sacrificed a piece to get a strategic advantage.
He needed a piece of granite.
Word: "piece"
different meanings

The story is false, so far as I can discover.
I discovered how to do it.
Word: "discover"
the same meaning

Call a runner out.
Call a football game.
Word: "call"
different meanings