Fine semantic differences between "thus" and "therefore"

Solution 1:

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.

Solution 2:

From American Heritage Dictionary of the English Language, Fourth Edition

thus

• In this manner: Lay the pieces out thus.¹
• To a stated degree or extent; so. ²
• Therefore; consequently: Thus³ it was necessary for me to resign.
• For example: Few of the nation's largest cities are state capitals; thus⁴ neither New York nor Chicago is the seat of its state's government.

¹ not same: you cannot say lay the pieces out therefore.
² not same: you cannot say we've discussed three topics therefore far
³ this meaning is the same
⁴ not same: replacing it with therefore makes it a conclusion out of an example.

Solution 3:

It is raining (A), therefore the grass is wet (B).

• therefore emphasizes that A was the cause of B.

It is raining (A), thus the grass is wet (B).

• thus means that A results in B, but does not emphasize that A was the cause of B.

Notes

A sidenote about German: after discussing this with an Austrian, we concluded that:

folglich/in folge -> thus

deshalb -> therefore

also see:

• Can "so" and "thus" be used interchangeably?

• Avoiding stuffy language: "Therefore", "Thus"

• https://en.m.wikipedia.org/wiki/Syllogism#Aristotle