SSAA, and MSAA shouldn't really blur the image at all if implemented properly (without bugs.) They work by rendering the entire image or specific assets at higher internal resolutions and then using an average of the colors provided by the extra pixels to output to the screen as a single pixel, which makes the pixel transitions look smoother than they would otherwise. SSAA does this to the whole image, while MSAA does it only to those parts which require it the most.
Console games used to use MSAA (in the seventh generation), but because of the way game engines are designed these days, and because it might be worth it to just render the game at a higher resolution this has gone out of favor. Now console games mostly use crappy FXAA, temporal AA, or SMAA.
MSAA won't work on on things like foliage unless it is real geometry.