Therefore is used in introducing a conclusion that follows from what has been said previously.
You are drunk, and that makes you incapable of operating machinery. Therefore you shouldn’t fly a plane.
Thus means in this way. For example:
He waved his arms around thus. (speaker waves arms around in demonstration)
Extending that meaning, it can be used to introduce the intended consequences of an action:
I intend to eat less, and thus lose weight.
And stretching that meaning further it can, like therefore, indicate the conclusion of an argument:
Trees are plants, and plants are living. Thus we can see that trees are living.
To me at least, in the cases where they have the same basic meaning, the effect of therefore and thus is slightly different: therefore emphasises that the conclusion is an inescapable logical consequence of what goes immediately before; thus puts more focus on the argument as a whole and the way it leads towards the conclusion.