Q: Why Java do not distinguish methods based on their return value?

Only on class names and arguments list?

I think, it could be obvious from declaration:

void aa(){}
int aa(){}
to use it later in a such way:
int bbb = aa();
compiler could easily distinguish which function must be used here - int, not void...

Answer: Yes, in this situation compiler easily will find out which kind of function must be used.

But quite often a method can be called directly - just to do something, not to return some value. The return value is not important here:

...
aa();
...

In this case compiler can not find out which method must be used. And other programmer reading your program will be confused as well.