I've heard of hitboxes, then I heard of hurtboxes. They seem most relevant to fighting games. What do each of them mean and how do they differ?
In most games Hitboxes and Hurtboxes are the same thing. They both refer to the area on the entity in which you (or more specifically, your own hitbox/hurtbox) can come into contact with for selection (talk to, or to interact with), or dealing damage.
As an example, Minecraft hitboxes (or hurtboxes, as preferred) are indicated by the white wire-frames surrounding the mobs, and items. (The hitbox representation for the player is glitched in this image - caused by the 3rd person camera offset):
As you can see: interacting/swinging at the pig's head will yield nothing, as it is not within the bounds of the hitbox/hurtbox.
However, in other games, mainly fighting games, like Street Fighter or Tekken, they are different. The hitbox is the area that will hit the opponent (red area), while the hurtbox is the area that you can take damage from an enemy attack during your attack (green box):
In fighting games, in particular, a hitbox is the area of the screen that will do damage if it touches an enemy hurtbox. A hurtbox is the area of the screen where a character is vulnerable to attack.
In this image, the blue box is the hurtbox, while the red is the hitbox.
In other genres, hitbox is often used to refer to both the area of an attack, and the outline of a character used in hit detection.
A hit box is an area that you can hit stuff with: for example in minecraft, villagers hit boxes are not on the very top of their head. This means if you hit them there they will not take damage or knocked back but if you hit inside the box it will hurt him and kill him.