The engine, the tool, and the all-weather tires
You may have heard people call Unity and other tools "game engines". That's almost correct. The confusion here comes from the fact that we have three distinct things, and we call them all "Unity".
When you download Unity, as you'll do in a moment, you're downloading the Unity 3D game authoring tool. To use a car analogy, the authoring tool works like your auto body shop. You use it to design and build the car's chassis, its handling, and its sweet, sweet leather interior and boss rims.
Under the hood, the authoring tool uses the Unity game engine, which is like the driving force behind your game. Unless you work out a pricy licensing deal with Unity Technologies, you are not allowed to mess around with the engine itself, but the engine is the piece that makes your car run.
When you're finished designing your game with the Unity authoring tool, your content gets bundled with the Unity game engine, and the two of them are packaged together with an extra piece that enables the game to run in a certain situation. The analogy gets weaker here, but consider tires: you can add snow tires to your car so that it can drive in the tundra, or dune buggy tires so that it can drive in the desert. In this way, you package your game content with a certain target platform in mind: PC, Mac, iOS, Android, or one of the various home video game consoles.
