Important Definitions
Many of these terms are defined different ways by different people, below are the most widely accepted definitions for each term.
Fully Automatic: A fully automatic farm is any method of resource collecting which doesn't require any form of interaction from the play with the exception of loading the chunks where the farm is located. The exception of this rule is any instance where the player must continually load and unload various chunks in order for the farm to function, for example, the enderdragon XP farm. In this instance, the farm is considered and AFK farm.
AFK: An AFK farm is any method of resource collecting where the player must directly interact with the farm in order for it to function, but a person doesn't need to be controlling the player in the game. An example of this is would be a music disc farm where skeletons attempt to shoot arrows at the player, but the arrows hit creepers obstructing the path to the player.
Farms which require the player to hold a single mouse button (often left or right click) also fall under this definition because it's relatively trivial to hold down one button. Common methods include placing a rock or another heavy object on a key, or using the F11 trick. If a farm requires more complex actions from the player, this definition does not apply.
Semiautomatic: A semiautomatic farm is any method of resource collecting where only part of the process is automated as described for a fully automatic farm, and the rest must be done manually. For example, a wheat farm where the collection process has been automated, but the planting must be done by hand.
Some types of farms can have multiple components, each of which could be described as a different farm design. For example, a tree farm where the player plants saplings AFK and withers automatically harvest the wood. The convention for naming these types of farms is to use the name of the least automatic portion of the farm. In the prior example, the farm would be considered an AFK farm since all components of the farm are done at least AFK. It would be misleading to call the farm automatic (even though parts of it are automatic) because this implies that all parts of the farm work without player interaction.