Could someone please elaborate, when to use high and when highly?
I guess both can act as adverbs.

e.g.During an era when tensions in the US "ran high"
In the sentence, above, can high appears better than highly..

But how do we generally distinguish between the two?

thanks,

Good question. And tricky.

First, it is correct to say "tensions ran high". It is incorrect to say tensions ran "highly".

In this sense, high is being used as an adverb. It is similar to "fast". He ran fast and he jumped high.

Highly can also be an adverb, as you say, though it is generally used in different circumstances. It can mean "very" as in "highly overrated", or favorably, as in "He thinks highly of her."

I believe that if you pressed too hard, though, you would not find a really good, simple rule. For example, we say that the "it was a high-priced item" but a "highly paid worker". In some cases there are just particular conventions for particular uses.