Is it necessary, and why?
Would it somehow imply that either the distance/online course vs the full-time course weight different values?
What about executive/weekend-format courses?
Isn't specifying the qualification and institution enough?
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It makes no difference how you got your diploma, as long as the institution has the same rigorous standards for taking the classes say either online or weekends as the regular full-time program. The only thing that's relevant is that you have the diploma and that you can produce it on request. In this day of soaring university education costs, you need not apologize for taking courses online at a reputable university.
Put the diploma that you legitimately got from the university on your CV and if anyone asks, tell them that the university offered you the online option and you took it. You are not misleading anyone. Because there is nothing to mislead anyone about. FYI: I got my MBA from NYU through their evening program, and I never saw the need to mention the fact that I got it through their evening program. Those of us who work full-time in NYC simply don't have the luxury of being full time students. You may not have the luxury of being a full-time, onsite student and a reputable institution's online program is designed to serve capable students who are in your situation. Neither you nor the institution have anything to apologize for. If anything, both of you should be commended for making the extra effort.
Again, most employers don't care about courses let alone the course format. They care about diplomas and whether you have them.
I've only every been asked out of curiosity how I am completing my studies so for most employers I don't think it really matters. The only time I would see this being an issue is if you're studying at a prestigious university via distance. For example, whilst Harvard is very selective in who attends its university on campus it pretty much lets anyone in who pays for its distance course - thus I would guess most employers would be very keen to know how you got into Harvard and might feel deceived if you didn't clarify that point.
So if the above isn't the case, I don't think you need to include that information on your resume, unless you think employers may get the wrong impression ("I see that you're attending University X, but you've applied for a full time position; how will you make this work?"). As you mentioned, where you attended, what you studied and perhaps what your GPA is should be enough.