Hi Dinghui, I have never seen or hear the words "sate" before. It seems to be quite an outdated word! To satiate is to satisfy a need or desire. I had to drink 1L of water before my thirst was satiated! Hope this helps!

According to google ngrams, ‘sate’ was more popular than ‘satiate’ for several decades but has been less popular since 2005. To me, ‘satiate’ sounds more positive, whereas ‘sate’ sounds better with a desire that isn’t wholesome. Eg, satiate one’s thirst, but sate one’s bloodlust. But I don’t have any corroboration of this theory.

Personally I have only used "satiate". I checked the dictionary and found that "sate" has similar meaning as "satiate". So I guess there is no difference. The way to find out is when you use the word and someone says that it does not sound natural. it's good to use words, make mistakes and learn.