Why there is a difference between Israel and the Church

Some try to merge the Church into being the same or somehow tied into being Israel. This is denied by a passage like it is here:

Heb 13:12  Wherefore Jesus also, that he might sanctify the people with his own blood, suffered without the gate.
Heb 13:13  Let us go forth therefore unto him without the camp, bearing his reproach.

There is a difference or there would be no reproach. The Apostle Paul was constantly being persecuted because of this. There is a clear difference.