Is there any character like that?

[nablator]

What is the list of all twins, and what is the difference I should look out for? 

Some people have been fixating on some tiny differences that they believe are meaningful. Nobody agrees on anything at this level of detail. Your guess is as good as anyone else's.

There is no way to identify variants unambiguously because their shapes are in a continuum, like spaces. Nobody can make an accurate unambiguous transliteration.