FXAA causes a lot blurring on the whole screen, so it is more complained about, but all forms of AA cause some form of blur. MSAA is more precise on what it blurs. It blurs the edges of objects, and only the edges, which are the most obvious forms of aliasing. SSAA blurs the whole screen, but with help from the game, it won't blur text and as it gets more information than FXAA, it blurs less.
But yes, AA is a blurring technique to disguise jagged edges.