Sick is the less formal of the two words. It usually describes short-term diseases. Ill is more formal and is used to describe long- and short-term diseases

In American English these two words are fairly close in meaning. In British English, 'ill' is the opposite of 'well', while 'sick' refers to vomiting and nausea. In British English, to 'feel sick' means to feel nauseous, and if you say 'I was sick' we would understand that this meant that you had vomited. However, in the context of employment, we do use terms such as 'off sick' to mean being unwell in general.

They mean the same thing.

Sometimes they are interchangeable, but other times not. Sick (sickness) deals with the physical temporary state ( cold, upset stomach, flu, virus, ailment, etc ) Ill (illness) deals with a long term effect ( cancer, HIV, mental health, and other diseases)

to be/feel sick/ill means the same thing - to be unwell, both for long and short times, but "sick" can also mean to vomit.