Hola Raul,
Como la diferencia en espanol entre " sujeto,tema, argumento (subject) , " y "asunto, cuestion"(issue)
Look , they both could mean 'tema' and could be used interchangeably in some contexts and wouldn't be synonyms in other.
The following are examples to show you when they could be interchanged and when not:
A subject of a conversation, book, painting ,photograph etc.. refers to all what it is about ,what it handles and tickles.
A subject is the matter of conversation as in 'change the subject" ( cambiar el tema).
An issue could also mean 'tema' ,the topic or what matters ,the subject of conversation but you can't say ' change the issue' and mean 'cambiar el tema'.
You could say "That's not the issue " (no se trata de eso)and you could also say "That's not the subject we are talking about..".
As an expression you could say ' at issue' and it means 'en cuestion' ,however you can't interchange it with 'subject' as in ' at subject'.
Those are kind of expressions where another word wouldn't give the same meaning if used instead, even if it means the same if used separately.
You can avoid or tickle a subject or an issue and here both mean 'tema' and could be interchanged.
If you say "to make an issue of something" it means ( sagar algo de quicio) and you can't use 'subject' instead to indicate the same meaning.
As an expression you also say " on the subject of ..... " ( a propósito de ... ) ,and you can't use ' issue' instead.
At university a subject means 'asignatura' ,so it is not an 'issue' of course in this context.
When 'issue' means 'cuestion' you can't interchange it with the word 'subject' as in :
" I was earning a lot of money,but that was not the issue". (ganaba mucho dinero, pero ésa no era la cuestión ). Here it is an 'issue' and you can't say 'was not the subject' ,because it is about 'cuestion' .
The same with :
"His integrity is not at issue " ( no se está cuestionando su integridad ).
You can't use 'subject in this context ,where it is about questioning something.
"We need to address this issue." Here you can use 'subject' as well to refer in both cases to " tenemos que tratar este asunto or esta cuestión or este tema ".
I hope those examples kind of give you an idea how to distinguish between using both 'subject' and 'issue' in different contexts.