Yeah, alignment, like camber/caster/toe is suspension parts related. Hence it should be done: 1) on new car (factory alignment has broad range of "pass"), 2) when you change suspension parts, 3) when you want some different settings (eg. more negative camber for track), 4) after crash or big hard shocks to suspension when you suspect alignment might get out of whack.
Balancing is for wheels+tires, so that wheel doesn't act as excentric crankcase producing vibrations when rotating, by large extent lessening comfort, adding roadnoise, reducing grip, reducing high speed stability, adding wear to dampers/bushings (but mostly of course due comfort). Should be done in most cases when you remount tires on wheels (not when you mount to different wheels+tires, as they are balanced as unit). That is 1) when you buy and install new tires on wheel, 2) when you change due season summer <> winter rubber, 3) and - your case - if you are informed, that some balancing wheights fallen of / if you feel something happened wrong with balancing (eg. unusual vibration/roadnoise) / or you tracked car that hard, that pieces of thread had been ripped off unevenly, and still want to use those tires
