Etymologically, Deepavali is a Sanskrit word meaning row of lamps (Deepa means lamp). Diwali is a colloquial form used in Northern states of India, as the word in their language for a lamp is Diva/Diwa.

Ultimately, there’s no difference as every Indian state has its own language so it’s all nitpicking. Because I’m a bum, I like to point out that South Indian (where I’m from) and East Indian states use the etymologically correct name, Deepavali.