Different nuance between “on + (Object)'s order” , “by + (Object)'s order”

Question

I'm taking this money on my uncle's order.

I'm taking this money by my uncle's order.

What is the difference between those two sentences above, and which one would a native English speaker use or widely use?

Answer 1

I would say there is a difference. "On my uncle's order" means "because my uncle told me so". "By my uncle's order" means "my uncle's order empowers me/gives me the right to"

Answer 2

You do something by someone's order, so it should be:

I'm taking this money by my uncle's order.

To have different nuances you would need to use a different verb. Other ways of saying it from the less pressing to the more pressing.

• at his wish
• at his instruction
• at his bidding, at his command, at his demand (they seem pretty equal to me but someone please rectify if I'm wrong)
• at his behest