die Fete
party
An informal, often cheerful and lively celebration or party. The word is mainly used colloquially.
Am Samstagabend machen wir bei mir zu Hause eine kleine Fete.
On Saturday evening we're having a small party at my place.

party
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party
An informal, often cheerful and lively celebration or party. The word is mainly used colloquially.
Am Samstagabend machen wir bei mir zu Hause eine kleine Fete.
On Saturday evening we're having a small party at my place.

'Fete' is a loanword from French ('la fête'), which means 'das Fest' (festival/celebration) or 'die Feier' (celebration). This origin explains the meaning and the rather relaxed, cheerful connotation of the word.
Wir organisieren eine Fete zum Semesterende.
We're organizing a party for the end of the semester.
The word 'Fete' (party) is used almost exclusively in colloquial language. It sounds more relaxed and informal than 'Feier' (celebration) or 'Party' (party).
Kommst du am Freitag zu meiner Fete?
Are you coming to my party on Friday?
Common colloquial verbs used with 'Fete' (party) are 'eine Fete machen' (to have a party) or 'eine Fete schmeißen' (to throw a party). 'eine Fete veranstalten' (to organize/host a party) sounds somewhat more formal.
Mein Nachbar schmeißt schon wieder eine laute Fete.
My neighbor is throwing another loud party.
party
'Party' and 'Fete' both mean a casual celebration with fun and often with music, food, or drinks. The difference is mainly in tone. 'Party' is very general and fits many everyday situations. 'Fete' is more colloquial and often sounds especially relaxed or a little cheeky. 'Fete' is used more among friends or in informal language, not so much in official texts. In terms of content, both words can often describe the same situation.

Meine Schwester hat gestern eine Fete mit ihren Freunden gefeiert.
My sister had a party with her friends yesterday.
Die Musik der Party ist bis in den Garten zu hören.
The music from the party can be heard all the way into the garden.