They mean almost the same thing so you can use them interchangeably. For example, if you said "One time I fell off a horse and broke my leg," you could replace "one time" with "once" and the sentence would have the same meaning.

Hmm - that question made me think ! For several of the meanings of once - you can use them interchangeably. 'One time' is used to emphasise that it was one time only, or that you are referring to one particular time. You can't use 'one time' when you are using once to mean 'after', such as 'once I had done the dishes, I could watch TV', or in the phrase 'at once'.