How can we have different answers? Well, it’s because technically what is sold as an “impact driver” is really just a form of an impact wrench. But, the market for the smaller, cordless impact wrenches has taken on a life of it’s own. To differentiate them, they are called “impact drivers”.

Let’s improve the slightly long answer:

an “impact driver” is usually meant to mean a smaller, often cordless, version of an “impact wrench.” Impact drivers generally sport a 1/4″ hex chuck that accepts driver bits, while impact wrenches use a 3/8″, 1/2″, or larger square drive for attaching sockets.
Impact drivers are usually electrical – lately mainly battery powered. An impact wrench is usually corded, if electrical, or driven by air pressure (pneumatic). Thus, a wrench is usually much more powerful.