Ordinary English has one word, full, for a whole family of sensations. Research writing on eating needs more than one, and it has developed a small vocabulary that is worth knowing simply because it makes the writing readable.
The central distinction is between the process that brings a meal to an end and the state that follows it. They are separate, they are measured differently, and mixing them up makes a paragraph incoherent.
Satiation and satiety
Satiation is the within-meal process: the gradual decline in the drive to keep eating that leads to stopping. It is studied by looking at what happens during the meal itself, including its length and pace.
Satiety is the between-meal state: how long it is before eating begins again, and how much is eaten then. The two can move in opposite directions, which is exactly why the vocabulary separates them.
Appetite as a broader term
Appetite in this literature is a broader word covering the desire to eat generally, including its non-hungry varieties. It takes in the pull of a particular food, the effect of company, and the ordinary rhythms of a day.
It is the least precise of the three terms and the one most likely to be defined afresh at the top of a paper, which is a reasonable signal that the field has not settled it.
Why the distinctions matter to a reader
Popular writing tends to collapse all three into fullness, and a finding about one then gets reported as a finding about another. Keeping the terms apart is the quickest way to see whether a summary is describing what was actually looked at.
None of this vocabulary tells anyone what to do. It exists to make careful description possible, which is a different and more modest ambition.