I take that to mean that if the spirit of God lives in a person then they are in the realm of the spirit and those that the spirit doesn't live in are in the flesh realm... in other words ALL saved people walk in the spirit and unsaved people walk in the flesh.
Yes...2 different realms completely. We still have the flesh with the law of sin still in it but the inner man in Christ has been circumcised by Christ where the body of sin has been "cut away" from the new creation that is in Christ. Col. 2:11
Paul calls it the circumcision of the flesh and heart. This is the circumcision of Christ when we receive Him after hearing the message of Him - where we are "sealed" by the Holy Spirit. Eph. 1:13
Religion always gets the gospel and the things of God backwards. They will say "Stop doing the works of the flesh and we'll be walking by the spirit.
It is the complete opposite of that - it is "walk by the spirit and we will not fulfill the lusts of the flesh to do "it's" desires." Gal. 5:16-17