'Anlamiyorum' means 'I don't understand' while 'anlayamiyorum' means more to 'I can't understand' (it's like you miss some point of an explanation, or someone explains something which is not clear enough)

anlayamıyorum is disability of understanding anlamiyorum is negative of understanding I am unable to understand I am not understand

'Anlayamiyorum' means 'I can't understand' and its positive version is 'Anlayabiliyorum'. But if you want to say 'I don't understand' it is 'Anlamiyorum'

Difference between both languages, I am not understanding is possible in turkish. But not in english. This causes some confusion as well.

I think, this translation is not correct. I don't understand means "anlamıyorum" I can't understand means "anlayamıyorum"