Interesting! I think we have to look at the tenses in which we use the verbs. In the present continuous : "Get him, he's running away!" This means "escaping". I can't think of a sentence with "He's running off" In the past tense, I think there are slight differences between the two verbs. I would say that" running away" is more calculated. "They ran away to Spain to get married" "My dog ran off and I haven't seen him in 2 weeks" "He ran off with some girl he'd just met" "Running off" may be more spontaneous, less calculated.

There is no major difference. Both suggest leaving abruptly to an unknown destination. You could additionally use run off as in "I ran off my boyfriend with my jealous ways" (meaning I was the reason he left me) Here's a link: https://ell.stackexchange.com/questions/80345/what-is-the-difference-between-run-off-and-run-away