The first meaning or spelling you find in the dictionary is the preferred one. The first definition of “presently” is “soon, in the near future.”
“Currently” means “now, at the present time.”
Many people use “presently” interchangeably with “currently,” because, most likely, they are thinking of “at the present time.”
I prefer to make the distinction between these two words. As always, though, common usage will be the deciding factor.