The difference in purely linguistic. It depends on whose language one is using to spell the word. There are three important options:

1. The language of British colonizers (Jembe)

2. The language of French colonizers (Djembe)

3. The language of the indigenous peoples (No written standard)

I choose not to celebrate colonization - the brutal takeover of other people’s land, lives, and culture for political and economic gain - by using the colonizer's words when I can find indigenous words that will communicate as well or better.

As I use it, the word, "Jembe," is a phonetic interpretation of the indigenous word for that drum.  Every one who can read it can pronounce it (unlike Djembe).  "Jembe" does just happen to be the same way that the British spell the word...but that's not why I use this spelling).