Do both mean exactly the same or do they have slightly different meanings?
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Personally I would put more of a regular scheme to frequently, as the word comes from the same stem as frequency (a sine curve of certain wave length, therefore repeating itself in a certain pattern). Often would denote more of an irregularity.
Maybe this is a déformation professionel, as I am programmer with a math background, or I derive it from German and Latin languages, for example French:
fréquenter quelquechose would mean to regularly go somewhere.
Therefore I would hear this
In colloquial English, they mean the same thing. Remember the pun in The Pirates of Penzance (which only works in British English): "When you say 'often', do you mean 'often' 'someone who has lost his parents' or 'often' 'frequently'?"
If there is a difference, it is that "frequently" describes a periodic relationship with an ongoing action, while "often" means a lot of times during the defined period. In effect, it's the same thing, just a very slightly different flavor.
First of all, although the meaning is essentially the same, to the point of one being used as a definition for the other in some dictionaries, often is an order of magnitude more common than frequently. Secondly, they occur together (collocate) with different words.
I can't see a clear semantic pattern to the collocations, but it does seem that the strongest collocations for frequently also commonly co-occur with often, but the strongest collocates for often usually don't go with frequently. This suggests that often has a broader meaning that includes frequently but goes beyond it.