What is the difference (if any) between a postdoctoral fellow and a postdoctoral intern? Are "fellowship" and "internship" synonyms? Is there a different meaning in this language, between North America and English-speaking Europe?
Sometimes there is none, depending on the field or college.

In the UK, there can sometimes be a distinction. There are certain postdoctoral researcher positions that are positions in a PI's group where one works under a professor or more permanent faculty. A fellowship in the UK system means one has research independence and is allowed to pursue her own research program freely. Sometimes postdoc interns can also do this but it depends on the field, program, and position.