small and large C value and variance

Please I want to know How does having small C value which means : Small margin of error is resulting to High variance I think it s the opposite since the errors will decrease so variance between classified data will decrease >>>>

and the case is same in large C value: wider margin will allow to wider range of errors and different data points will be included so the variance should be higher not lower

if i misunderstand any of the concepts tell me

thanks in advance