Adherence vs Obey - What's the difference?

As a noun adherence

is adherence.

to do as ordered by (a person, institution etc), to act according to the bidding of.

* (archaic)

A close physical union of two objects.

Faithful support for some cause.

(medicine) An extent to which a patient continues an agreed treatment plan.

(en verb)

To do as ordered by (a person, institution etc), to act according to the bidding of.

To do as one is told.

(obsolete) To be obedient, compliant (to a given law, restriction etc.).

* 1590 , Edmund Spenser, The Faerie Queene , III.iv:

They were all taught by Triton, to obay / To the long raynes, at her commaundement [...].

* disobey * defy * rebel * resist * violate (especially rules )