tool size concept- tool path generated vs gcode

please explain to me why the tool size is defined in the tool path software which determines the actual path, but later in mach3 it asks about the tool size. is it possible to use a different sized tool and not have to rerun the tool path software? i see there are provisions in mach3 for worn/resharpened tools, but if i create gcode for a say 1/2" endmill, can i run that code with a 1/4" endmill? if i mistakenly try to use, say a too large of a tool, will i get error warnings?