Difference between "act according to" and "act under"

Question

“In particular, acting under orders caused participants to perceive a distance from outcomes that they themselves caused,” said study co-author Patrick Haggard, a cognitive neuroscientist at University College London, in an email.”

From https://www.pbs.org/newshour/science/how-the-nazis-defense-of-just-following-orders-plays-out-in-the-mind

What is the difference between "act under" and "act according to"? If I change "acting under orders" to "acting according to orders" here, would any nuance be lost?

I originally asked the same question here (https://forum.wordreference.com/threads/act-under-according-to-orders.3589389/#post-18265641), but sadly I didn't get a valid answer. I hope you can help me.

Under: subject to the authority, control, guidance, or instruction of

According to: In conformity with (Merriam Webster)

Answer 1

It's a fine distinction, and most of the time we'd see the two forms as synonymous, but I think the difference is implied by the two definitions as cited by OP.

Generally speaking, if you're acting under order[s], the implication is you've been given a specific order to do whatever it is.

If you act in accordance / accord with orders, or according to orders, this could often simply mean that the way you're doing something doesn't break the rules (i.e. - is legitimate). You haven't necessarily been specifically instructed to do whatever it is.