Why did prophet Muhammed (peace and blessing of God upon him) order us that we must differ from Christian and Jews?

This means to be different from them concerning the things which are part and parcel of their beliefs and are at odd with Islamic law. This does not include contradicting them in everything. Ibn 'Abass (may God be pleased with them) narrated, "The Messenger of God (peace and blessings be upon him) used to let his hair loose, while the disbelievers used to part their hair.

The people of the Book [Ahl al-Kitab] used to let their hair loose and the Messenger loved to be in compliance with them as per the matters which are left open in Islamic law. Then the Messenger of God used to part his hair".

(Bukhari)