There are different types or kinds of Israel. These can be brought under two main categories.

“For he is not a Jew, which is one outwardly; neither is that circumcision, which is outward in the flesh: But he is a Jew, which is one inwardly; and circumcision is that of the heart, in the spirit, and not in the letter; whose praise is not of men, but of God.” (Rom 2:28-29, KJV)

Two broad categories of Jews or Israel are mentioned by Paul from the scripture above:

• Outward Jews. These are Jews with physical circumcision accouding to Abraham. These were circumcised by men. Here, we hav so many kinds of Jews such as Proselyte Jews who were gentiles but became new born into the Jewish nation by water baptism after which they undergo physical circumcision. Here, we also have those who are direct discendants of Abraham through Isaac. We also have Children of gentile women such as Ruth and Rahab who married Jews and gave birth to children who also had physical circumcsion. All these make up the Israel after the flesh

• Inward Jews. These are Jews with inward circumcision according to Abraham. These are Jews or Israelites not circumcised by any man; Jesus Christ circumcised them by the spirit of God. They went through divine operation.

Col.2:11 puts it this way saying that "...are circumcised with the circumcision made without hands,...". This scripture went further to decribe their circumcision as "...the circumcision of Christ:...". To show that it was not a circumcision made by any human, Col.2:12 says it is "...the operation of God..."

Who make up the Inward Jews?

These are made up of Gentiles who have had inward circumcision as well as Outward Jews who have had inward circumcision. These make up the church of the living God.

“Having abolished in his flesh the enmity, even the law of commandments contained in ordinances; for to make in himself of twain one new man, so making peace;” (Eph 2:15, KJV)

God created to himself 'one new man' via his own operation.

Those who have had inward circumcision are the Israel of God This is the church of God. Heb.12:22.

If we look at the context of Gal.6:16,

“For in Christ Jesus neither circumcision availeth any thing, nor uncircumcision, but a new creature. And as many as walk according to this rule, peace be on them, and mercy, and upon the Israel of God.” (Gal 6:15-16, KJV)

Paul says, "..as many as walk..." Who are these? They are the new creature in Christ Jesus. There is a rule they are to walk or live their lives in accordance to - the rule of the new creature.

In Christ Jesus ....circumcision, that is, physical circumcision or being an outward Jews produces no effect. Likewise, uncircumcision, that is, obedience to the law via conscience by the gentiles produces no effect. Hence, the lifestyle of the inwardly circumcised and their mindset is conspicuously different from that of the outward Jews and that of the gentiles. This is the bedrock of Gal.3:28:

“There is neither Jew nor Greek, there is neither bond nor free, there is neither male nor female: for ye are all one in Christ Jesus.” (Gal 3:28, KJV)

The identity of Israel after the flesh is undressed as well as the identity of the Gentile. By virtue of inward circumcision done by God himself, a person puts on Christ.

Those who put on Christ by the operation of God are the Israel of God. Every God-circumcised individual is an Israelite of God.

And...every man-circumcised indivdual but not circumcised by God is an Israelite after the flesh.