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.
According to Dorland's Illustrated Medical Dictionary, 30th ed, resolve is defined as: "to restore to the normal state after some pathologic process."
So in this illustration, resolved means that the pathologic process has been stopped, and the normal state has returned.
Improved means that the pathologic process is no longer progressing and the condition has moved more toward the normal state, but is not there yet (or may never get there).
Reduction is used in its usual sense here: the amount by which something is lessened. In the illustration, it is used for a lessening of a risk (of cardiovascular disease) and of a rate (of mortality).
One thing that is not clear, based on the information provided in your question, is what the percentages are actually percentages of, and why some of them list ranges. (Perhaps the range is because the illustrator is citing data from multiple studies). I would guess that most of the conditions listed as resolved or improved are a percentage of the people who had the condition, who then lost fat and no longer have the condition or the condition is improved. For example, losing fat resolved the obstructive sleep apnea in 74% to 98% of people who had sleep apnea before losing fat. (The flip side is that losing fat did not resolve the apnea in 2% to 26% of people.)
Best Answer
“Usage note: presently. In both British English and North American English, presently can mean ‘soon’ or ‘after a short time’: I’ll be with you presently. In North American English the usual meaning of presently is ‘at the present time’ or ‘now’: She is presently living in Milan. ◇ There is presently no cure for the disease. This use is becoming more accepted in British English, but at present or currently are usually used.”¹