Difference between "sick" and "ill"?

Is there any difference between “sick” and “ill” ?

Is “sick” mor slang/familar whereas “ill” more official ?

Describes “sick” a more temporary state whereas “ill” is a permanent (e.g. 3 weeks) state ?

In the sense of poor heath, disease, etc, they are essentially the same in AmE; ‘sick’ is more frequent, because ‘ill’ is considered a bit formal.

I understand that in BrE, ‘sick’ more often means nauseous, bored, frustrated or other non-disease-related weaknesses, and ‘ill’ is the usual term for physical problems.