they are very similar and can sometimes be used interchangeably.
That having been said, "intent" is used more often to describe a person's internal thinking behind their actions. For instance, if a person runs over another person with their car, you might have to wonder if they did it "by accident" or "with intent" (that is, on purpose).
Another example; "purpose" tends to be the word we use more often to describe the point of a thing in itself, e.g. "The purpose of the new highway is to reduce traffic". On the other hand, you might say "The highway designers' intent was to reduce traffic" since you are talking about what the designers had in their minds.