Question :
Is Tamayyuz and Al-wala Wal bar'aa are two same things or between them there is a difference ?
وعليكم السلام ورحمة الله وبركاته
You should know that Tamayyuz (distinguishing one's self from others) is a branch of Al Walaa wal Baraa' meaning that there is a (relationship of) generality and specificity between them from one perspective , and there is agreement between them from another perspective.
For example , you should have Walaa' (loyalty) towards your Muslim brother as long as he is a Muslim , and this is a general Islamic brotherhood as mentioned in the saying of Allah عز وجل ( the believers are nothing else than brothers ) إنما مؤمنون إخوة .
But from another perspective you should distinguish yourself from him if he is committed to a sin or some kind of innovation whilst not wasting away the general allegiance or loyalty that he deserves since he is a Muslim . Therefore you should free yourself from those sins and innovations and you should show him that you do not agree with him in it but at the same time you should also believe that he is your Muslim brother in general .
So it is necessary to understand the correct relationship between Tamayyuz and Al Walaa wal Baraa and the confusion regarding this will make you fall into one of the two extremes "exaggeration" Ghuluww and "leniency" Tamyee'.
So you must know that the absolute Tamayyuz which is absolute Baraa' in every way is only with those who are enemies to Allah عز وجل and His Messenger صلى الله عليه وسلم . As for those who disagree with you whilst they are still within the circle of Islam, then there is detail regarding how to deal with them ( and it is not absolute and unrestricted ) .
And Allah عز وجل knows best .