My guitar only has one set of volume and tone controls. Does this mean I cannot use distortion?

The distortion works when I press a little button on my Amp. However
it does not work with my guitar which only has 1 set of volume and
tone controls but it does work with my other guitar which has 2 sets.
Therefore this proves that the amp isn't broken. Also the guitar with
only 1 set works perfectly well with the amp without distortion so it
can't be the guitar either so this is why I think that my guitar
doesn't work with distortion. Am I correct?