There is the choice of either muting all of the strings or muting those that are undesired while still enabling some to sound out. I find the latter technique useful especially if the original chord that I am playing has an open string in it that I would have played in the next chord. With this technique, though I am muting certain strings in preparation for the upcoming chord, I am still theoretically keeping this open string sounding out so that, if I am careful enough, it can keep resonating through the next chord too.