There is considerable overlap, but in general mystics tend to be much less powerful than sorcerers.
Mystics tend to be characters in street-level or slightly above stories. The Hand is generally what I think of when I think of mystics. Subtle low-end magics that make them slightly better at stealth and assassination than is humanly possible. Slow, complicated, rituals to raise the dead being their high-end.
Or to use a tv example, the resurrection of White Canary is a perfect example of what I think of when I think of mysticism. A slow, dangerous ritual using a precious resource that brings one person back from the dead at great cost and risk.
Sorcery is things like you see in Doc Strange and Harry Potter. Flashly, nearly instant, reality-warping stuff.
It's telling that characters like Fu Manchu used to be called a mystic. Fu never did anything flashy. It's just implied that he subtly amplified the products of his science with barbarous asian mysticism.
The villain in "Indiana Jones and the Temple of Doom" is a mystic.
I'd say the highest you get with mystics is the sort of thing you saw in original Conan stories: slow, dangerous, costly rituals to summon chthuluesque horrors.
Generally, if a character mostly relies on mundane military force and his magicks subtly benefit those mundane forces, the character is a mystic. If the character can casually throw down with flashy blasts, he's a sorcerer or wizard.