Use of "the ill" vs. "the sick"

I was struck by the use of "the ill" as a noun phrase in a sentence from a question asked yesterday: "I'm going to be a doctor. I'm going to help the ill." For some reason, I felt that "the sick" would be much more natural here. I tried searching Google for further examples of "the ill", and I found some uses that seemed more natural, but that also seemed a bit different to me:

• The Church and families of the ill, infirm and dying have a very important role to play

  ("Anointing of the Sick", The Cathedral of Saint Thomas More)

  (Here, "ill" is used along with two other adjectives, "infirm" and "dying"; but "the sick" is used many times in the rest of the page)

• The sacrament is administered to give strength and comfort to the ill and to mystically unite their suffering with that of Christ during his Passion and death.

  ("Anointing of the sick", Encyclopaedia Britannica)

  (I don't know why, but for some reason "the ill" sounds OK to me in this sentence, even though I found it jarring in the "doctor" sentence. I think it could be a matter of register: the Britannica passage seems to use fairly elevated language, whereas the quote that bothered me was attributed to a child speaker and used contractions ("I'm"), which are not as common in higher registers of the language.)

I couldn't find any information about the use of "the ill" in the Oxford English Dictionary. Is it just a synonym for "the sick", and if so, does the use of one vs. the other differ between different varieties of English?

I know that British English speakers often use be ill instead of be sick, because be sick has come to be used in some contexts to mean "vomit". But the Google Ngram Viewer seems to indicate that "help the ill" is not yet clearly established as the main variant in the UK.

The frequency of "the sick" when not followed by a noun is somewhat greater than the frequency of "the ill" when not followed by a noun in the British English Ngram corpus:

The frequency of "help the sick" is much greater than the frequency of "help the ill" in British English:

Solution 1:

It is correct to use ‘the ill’ as in ‘I'm going to be a doctor. I'm going to help the ill‘ - but use of ‘the ill’ has declined in popularity, in comparison to ‘the sick’, which is why it sounds odd or unfamiliar.

‘Ill’ has another meaning, which is ‘evil or bad’ as in ‘ill will’. Or ‘he thought ill of her’ (meaning, he thought badly of her’) which now sounds a bit archaic in some contexts but would also still be understood.

Sick does indeed also mean ‘to vomit’. ‘The sick’ or ‘the ill’ are similar in meaning.

‘Ill’ can be about ‘the mind’ as in ‘mentally ill’.

Whereas ‘sick’ tends to be about the body. Although not solely - as in ‘a sick mind’.

Etymology

‘Ill’ is from Old Norse ‘it is bad to me’, evil, difficult

‘Sick’ is from Old English sēoc ‘affected by illness’

https://www.etymonline.com/word/ill

https://www.etymonline.com/word/sick