Learn English – the difference between a question and an invitation

I think command / invitation is a dichotomy much the same as desirability / probability as recently explored by this question.

IMHO you will not find 'rules' unambiguously telling you how distinguish between modes of command, invitation, permission, expectation, etc. because speakers frequently wish to blur those distinctions.

At one extreme is simply the wish to avoid giving offense, by couching a command as an invitation. At the other is the domineering tactic of a powerful person assuming that his slightest indication in favour of some particular outcome should be taken by his underlings as a direct command to progress things in that direction.

Human interaction is the primary function of language, and the dominant / submissive juxtaposition is one of the key elements of that interaction. All of us 'bend' language in this area from time to time to suit our own agenda. And over time, all of us unconciously connive at making sure the language is easily bent in this area.

In short - if you want to identify structural differences between a command and an invitation, you'd do better to ask a psychologist rather than a grammarian or linguist.

Something illegal is forbidden by law: "It is illegal for motocyclists [sic] not to wear a crash helmet."

If a thing is illicit it is done by someone who knows that it is disallowed by law but that under different circumstances it could be legal: "The crew were involved in the illicit import of brandy"

(it is basically legal to import brandy but not the way they did it).

This is backed up by things like illicit sexual relationship. It's not wrong to have a sexual relationship normally, but it could be "wrong" if you are married, or not yet married, etc. illicit trade is another such example. It's not wrong to trade, unless you do it in the wrong way.