My understanding is that J'ai mal à + noun is physical pain whereas Je suis malade is more like "I am sick" (perhaps with a flu or cold). Can you please confirm whether that is correct?
As well, it would probably be useful to either link to a lesson that explains être malade or have another section in this lesson that explains the difference for future students!
You are correct in your understanding.
The reason not to introduce the expression -
être malade = to be ill/sick
is that it is literal, uses a different verb which might confuse some students at that level.
Avoir mal à is a very useful expression to learn as it introduces different parts of the body and être malade is very general.
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