You know this situation: you find yourself in a (heated) discussion about a topic, going around in circles and becoming louder in telling the other one is wrong - only to at the end find out that you and your counterpart are talking about the same thing. The same thing, context, solution – just in other words.
There are 2 hurdles we need to discern here:
1. Communication Hurdles
2. Hurdle of different perspective
As for communication, there are various models highlighting the stages of communication and the hurdles between issuer and receiver eg. Interactional Model, Transactional model or Coordinate Management Model of Meaning. The latter one involves 7 stages, including cultural background and relationship between communicators – so there are many ways to go wrong!
As for the different perspectives – we create or renew our reality continuously. So, there is ample chance, that you and your counterpart perceive this “reality” identically or even similarly.
So next time you sense there is a sort of misalignment in a discussion, act as follows: 
Ask yourself: Is this a communication hurdle where our cultural background or vocabulary prevent us from a clear understanding? 
Or are my counterpart and myself looking from different viewpoints at the topic at hand – and is the path to understanding easier if I try to take his stance?
I am curious to hear about your experiences!