Occultism and Mysticism

What is the difference between occultism and mysticism?

They are not at all the same thing.

Mysticism is a more or less emotive relation with what one sees to be a divine power—that kind of highly emotional, affective, very intense relation with something invisible which is or is taken for the Divine. That is mysticism.
Occultism is exactly what he has said: it is the knowledge of invisible forces and the power to handle them. It is a science. It is altogether a science. I always compare occultism with chemistry, for it is the same kind of knowledge as the knowledge of chemistry for material things. It is a knowledge of invisible forces, their different vibrations, their interrelations, the combinations which can be made by bringing them together and the power one can exercise over them. It is absolutely scientific; and it ought to be learnt like a science; that is, one cannot practise occultism as something emotional or something vague and imprecise. You must work at it as you would do at chemistry, and learn all the rules or find them if there is nobody to teach you. But it is at some risk to yourself that you can find them. There are combinations here as explosive as certain chemical combinations.

Ref : Questions and Answers 1954