What is the difference between presently and shortly? They seem to have rather similar meanings.
Presently has two meanings: currently and shortly. So, one difference is that shortly does not mean currently. Otherwise they mean pretty much the same thing.
Ngrams shows that shortly is more common than presently. If we take into account the fact that the results are context-agnostic and the fact that a fair portion of the uses of presently found by Ngrams was in the sense of currently, we can conclude that in the sense of soon the word shortly is far more common than presently.
Certainly the senses of presently and shortly overlap -- senses of the first include "Before long; soon", and senses of the other "In a short or brief time or manner; soon; quickly" -- but the sense "At the present time; now; currently" of presently is not uncommon, and the sense "of short duration" or "terse" of shortly likewise. In these latter senses, neither word substitutes for the other.
I say "not uncommon", above, because instances of presently with the meaning "at the present time" occur frequently in Google books but the meaning "after a short while" occurs more frequently.
ngrams for presently,shortly shows that presently was more common than shortly before the early 1800's, and mostly vice versa since then; but their frequencies do not differ significantly enough to allow any particular conclusions to be drawn.
I like the tone and content of the above responses. Yet, there may be a subtle distinction in use.
A social superior might say, "I'll be with you presently". But it would seem rude and out of place for a social inferior to say the same thing.
On the other hand, "I'll be with you shortly" appears socially neutrally. As likely to be used by an inferior or a superior.