Well, I have rarely ever seen denizen, so my guess is while probably interchangeable, citizen is much more commonplace, while denizen is probably much more scholarly and formal. Also, I think it's a difference of American versus British English, with denizen being found more in British English. It does seem that denizen is more often a foreign inhabitant. Here's also a more technical description in a forum: http://english.stackexchange.com/questions/33283/what-is-the-difference-between-citizen-and-denizen

I've only really come across this (I'm British!) when someone becomes a citizen (i.e. a foreigner coming over to live here becomes a "denizen"), and I think it also applies when a foreign plant species may become an invader to a particular area (i.e. a fungus may become a "denizen" of a particular forest). It's not a word that's used very regularly!

I agree with Christian - at least in the United States, I rarely hear the word denizen used, and if it is used, it will be in articles or scholarly writings. I don't think many people use it colloquially.

I wouldn't use "denizen." In the United States, it is NOT used as a synonym for "citizen." When it is used, the context is usually half joking. Someone is deliberately using a formal, academic word for some kind of dramatic or humorous effect. To use it seriously would be to write stilted, flowery, "purple prose." To be very specific, almost the only place I'VE ever heard it is used is in one specific stock phrase--"denizens of the deep," meaning fish and sea creatures. It is rather like referring to elephants as "ponderous pachyderms," or long words as "sesquipedalian polysyllabics." Actually, I guess this is the point where I need to mention an occult farrago whose phylogeny recedes into tenebrous nebulosity: the "announcer's test," http://en.wikipedia.org/wiki/Announcer's_test

Thank you all very much for your kind comments! I will study more!!