I never really liked "blindfolded cubing", since you can essentially practice the same activity without an actual blindfold (although it's not officially valid because you're not taking the extra time to put on the blindfold). To me, "blind cubing" is better, since you are describing the act of performing the solving of the cube without being able to look at it. So "blindfolded cubing" can only describe when you actually use a blindfold, but "blind cubing" allows that you might be solving it behind your back, under a table, with your eyes closed, etc.
I've taken to avoiding the issue by always typing "BLD cubing". Everyone in the cubing community knows what the abbreviation BLD means, and you can take it to mean whichever thing you want it to mean.