satt
full
The feeling of having eaten enough and no longer being hungry.
Nach dem großen Stück Kuchen bin ich jetzt pappsatt.
After that big piece of cake, I'm completely stuffed now.

full / fed up
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full
The feeling of having eaten enough and no longer being hungry.
Nach dem großen Stück Kuchen bin ich jetzt pappsatt.
After that big piece of cake, I'm completely stuffed now.

In the meaning 'nicht mehr hungrig' (no longer hungry), 'satt' (full) is almost always used as a predicative adjective. So you say 'Ich bin satt' (I am full), but rarely 'ein satter Mensch' (a full person). Another typical construction is 'sich satt essen' (to eat one's fill).
Danke für das Essen, ich bin satt.
Thank you for the meal, I'm full.
The expression 'etwas satt haben' (to be fed up with something) means that you are annoyed by something. The structure is always: person + haben + accusative object (what is annoying) + satt. This phrasing is colloquial.
Ich habe das schlechte Wetter so satt!
I am so fed up with the bad weather!
To describe a color as intense and strong, 'satt' (rich) is placed directly before the color. Typical combinations are 'sattes Grün' (rich green), 'sattes Rot' (rich red), or 'sattes Blau' (rich blue).
Der Himmel hatte ein sattes Blau.
The sky had a rich blue color.
full
'voll' and 'satt' can both have to do with the feeling after eating, but they are not the same. 'satt' directly says that you have eaten enough and are no longer hungry. 'voll' can also be used colloquially about your stomach or the feeling after eating too much, but the word generally means: something is filled. That is why 'voll' also fits bags, glasses, rooms, or buses. Learners easily confuse the words because after eating you can say that you feel full. Usually, the more natural thing to say is: 'Ich bin satt.' ('I am full.' / 'I have had enough to eat.'). 'Ich bin voll' sounds more colloquial and can also be ambiguous depending on the context.

Nach der großen Portion Nudeln bin ich wirklich satt.
After the large portion of pasta, I'm really full.
Nach dem Einkauf ist der Kühlschrank wieder voll.
After shopping, the refrigerator is full again.