Flying ants (ants with wings) and termites can look very similar. Both ants and termites have a very developed social class structure, with different types such as soldiers, reproductives, queens and workers. They both swarm, which means that they send out winged representatives from their colonies to mate with the opposite sex from other colonies and find new homes. They can wind up either being in close proximity to your home or actually in or about your home. However, there is enough difference between ants and termites to readily tell them apart.
One way to tell the difference between ants and termites is to take a close loom at their antennae. An ant's antennae will look elbowed on the ends, folding or bowing inwards and it will appear to be topped with a minute ball. The termite will have antennae that look like they are made up of strung-together beads and they will not be bent.
Geography and Habitat
Where you actually find an ant or termite in your house will be telling. Ants are going to be found in and around the kitchen, as they will be after any edible food they can find, especially anything sweet such as sugar. The termites won't be easily found at all, as they will be hanging out in the attic or in the rafters, living in and off of whatever suitable wood they can mange to get to.
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The shape of the termite's body is different than that of the ant. A termite has a "thicker" body, looking like it is composed of only two sections: a head and a thorax. The ant looks like he is made up of three separate sections: a head, a thorax and an abdomen. The "neck" and "waist" of the ant are thinner.
While both species that can fly have wings they will differ in their size. Both will have two sets of wings when they are mating or looking for a new colony, but the termite's back wings are easily discernable beneath the front ones; the ant's cannot be seen. This is because the termite has a pair of same-sized wings while the back wings on the flying ant are shorter than the front ones are.
Misconceptions about Ants and Termites
There is a general misconception, brought about mostly by cartoons, as to termites being able to go through wood like a chainsaw, eating you literally out of house and home overnight. Nothing could be further from the truth though. Termites can inflict plenty of damage on the wood in your house, but it takes them a very long time to do it, as they eat small bits each day. One thing that is true is that ants and termites are the worst of enemies and when they do battle put your money on the ant.
TL;DR (Too Long; Didn't Read)
Keep in mind carpenter ants vs termites when you are assessing damage to wood.