If I heard a VFR pilot say he's "going missed" I would assume he really means he is "going around" - i.e. aborting his landing attempt - and will fly the pattern and attempt another landing. At a controlled airport usually the tower will then issue either left or right traffic, or other instructions, depending on what else is happening. No matter if the pilot has been cleared for the option or cleared to land, at ANY time he may decide to discontinue the landing and "go around" - something on the runway, unstable approach, too fast, too high, a warning light, or just a bad feeling, it doesn't matter. Although I would try to add a reason if I weren't too flustered - "N123 going around, turtles on the runway" or whatever.
If an IFR pilot on an instrument approach says he's "going missed", I would expect he means he's aborting his landing and beginning the published missed approach procedure for the IAP he was flying, NOT entering the pattern. Tower usually then hands him back to departure control for further negotiations. However, if I were IFR on a visual approach, I would say "going around", not "going missed", and expect to enter the pattern for another try.
To me, "going around" means I'm planning on flying the pattern, and "going missed" means I'm planning on flying a missed approach procedure - at least until ATC changes my plans. But I'm a pilot, not a controller - that's just my opinion.