Why are "dynamic" and "deontic" modalities so called?

It is said that there are three types of modality: deontic, epistemic and dynamic.

Here are sample sentences for each type of modality:

(1) You can stay as long as you want. [deontic]

(2) You may be right. [epistemic]

(3) He can drive better than you. [dynamic]

The first two names are said to be derived from the Greek for "biding" and "knowledge", respectively.

As far as 'epistemic' is concerned, the meaning derived from the Greek is such that I can easily understand why linguists who coined these terms did so.

As for 'dynamic' and 'deontic', however, it's not as clear to me why 'dynamic' and 'deontic' are chosen to coin the term 'dynamic modality' and 'deontic modality', respectively.

Specifically, what's so 'dynamic' about sentence (3)? (3) represents the subject's ability. I mean, what has being 'dynamic' got to do with anything about the subject's ability?

And what's so 'deontic' about sentence (1)? (1) represents the speaker's permission, and not any sort of 'duty' as expressed by the word 'deontic'.

Hence these question:

What's the specific meaning of 'dynamic' in 'dynamic modality' that is descriptive of this type of modality?

Why use the difficult word 'deontic' when it doesn't actually represent the whole picture of the type of modality that it's supposed to represent?

The expression deontic is derived from the Greek deomai (δέομαι), translated request:

(1) You can stay as long as you want, implies permission.

The expression epistemic is derived from the Greek epistamai (ἐπίσταμαι), translated to know:

(2) You may be right, implies supporting knowledge.

The expression dynamic is derived from the Greek dunamai (δύναμαι), translated to be able:

(3) He can drive better than you, implies ability.

Linguists, like lawyers, doctors and many other professionals, employ obscure terminology from ancient languages so that they can control their definitions without interference from colloquial semantic pressures. The confusion surrounding dynamic seems to arise from a modern colloquial connotation which irrelevant to the modality descriptor:

adjective

1 (Of a process or system) characterized by constant change, activity, or progress:
ODO

etymology:

1817 as a term in philosophy; 1827 in the sense "pertaining to force producing motion" (the opposite of static),
from French dynamique introduced by German mathematician Gottfried Leibnitz (1646-1716) in 1691 from Greek dynamikos "powerful,"
from dynamis "power," from dynasthai "to be able, to have power, be strong enough," which is of unknown origin.
The figurative sense of "active, potent, energetic" is from 1856 (in Emerson). Related: Dynamically.
etymonline.com