Bhagavad Gita, Chapter 3, Verse 25

As the unwise act with attachment to their work, O descendant of Bharata, so should the wise act, but without attachment, wishing to guide the world.

The outward action can look identical, the real difference is what's actually driving it underneath.

Someone wise doesn't need to act differently from everyone else to prove a point, they can do the exact same duty, just without the personal grip on the outcome, and let that quietly guide others in the right direction.