Both insects swarm in spring, both shed their wings indoors, and both leave a small pile of them on a sill. Told apart, they mean completely different things: one is a structural emergency and the other is a moisture problem you have some time to solve.
Four wings, two sizes
A termite swarmer has four wings of equal length, noticeably longer than its body. A carpenter ant swarmer has four wings too, but the front pair is clearly longer than the back pair.
The waist settles it
A termite has no waist — the body is a straight tube from head to tail. An ant has the pinched waist you would draw on an ant. If you have a specimen and a phone camera, that is the photograph to send us.
