What's the difference between "to frighten" and "to scare"?

I would suggest that 'frighten' is more intense than 'scare'. Although they are (very) similar, being scared is less serious than being frightened. That is definitely a second-order effect though; to a first approximation, they are (almost) equivalent.

The two words are synonyms and may be used interchangeably. Scare comes the Old Norse word skirra meaning "frighten."

I would use frighten when I mean something with the hint of a surprise. Scare would mean something more gradual, as in "to scare with fear, uncertainty, and doubt (FUD)"

When I use frightened I use it like it has a bit of tense and suspicion in it. Scared just feels like it’s horrible and creepy. Also frightening is more severe than scared.