A century ago, presently was used to mean "now," a meaning that some writers and speakers still attribute to it. Presently is more precisely used to mean "soon," "before long," "directly," and "in a short time": "I will be there presently." Its use to mean "at this time" is debatable and inaccurate. Currently means "at the time now passing," "at this moment," "right now": "She is currently taking a bath." "I am currently far in debt." "Although I am currently not well, I hope presently to feel better."
Dictionary of problem words and expressions. Harry Shaw. 1975.