There are many different types of AA. In every case, there is some smoothing/blurring that takes place, but some are worse than others. MSAA typically does the least blurring, as it is very targeted, fixing only the outer edges of objects. Most post process AA methods cause the most blur, as they try to smooth everything on the entire image, and does not get any assistance on knowing what to target from the game engine. FXAA, SMAA, MLAA and TXAA are the worse in this regard. SSAA even does some blurring on the entire image, and it is extremely taxing to the frame rate.
Learning which AA methods tend to lead to your more preferred result would be helpful. Until then, I advise sticking with MSAA x4/2. Do not go higher, as it tends...