There are basically three things here. A drill, a hammer drill, and an impact driver.

A drill is exactly what you think it is, nothing more and nothing less. It looks like this.

A hammer drill is an upgraded version of a drill. Sometimes with a drill, to help get the screw or bit into the substrate, you'll have to push on the drill. Imagine that while you're drilling, some dude's standing next to you hitting the back of the drill with a hammer. That's a hammer drill. It looks nearly indistinguishable from a regular drill, but there'll usually be a little outline of a hammer on the side. The main takeaway is that you don't have to push as hard to get into something.

An impact driver is an upgraded version of a hammer drill. Imagine that in addition to the previously mentioned hammering action, the drill bit has a big X on it with the four lines at 90 degree angles to it. When it senses trouble turning the chuck, it's like four dudes start whacking those lines with hammers to help. That's in addition to the dude hitting the back of the drill with the hammer. Impact drivers look sort of odd; if you've never seen one before you'd assume it's a compact drill because it looks like one but with a shorter snout. In addition to being better for driving nails and bits, it's also really helpful for removing bolts and screws that're stuck. It's interesting because the sound is something like rrrrrrrrrrrrrrrrrrrBANGBANGBANGBANGBANGBANGBANGBANGBANGrrrrrrrrrrrrrrrrrrrrrrrrr with the bangs being the impact kicking in.

You should have a regular drill because sometimes you'll be doing work where you don't want the ability to be slow and gentle. Hammer drills and impact drivers will kick in their extra features automatically and aren't a great substitute for that reason. However, an impact driver is like a better version of a hammer drill, and there are few if any situations where a hammer drill would be a better choice than an impact driver. For this reason impact drivers are very often sold in pairs with drills but hammer drills need to be bought on their own.