Actually, I think the term "spiritual man" was taken from the Bible and was simply started to be interpreted in a different way.
So, let's begin. A spiritual person has a certain stereotype of thinking that is different from the type of thinking of the carnal man, this stereotype of thinking he received as a result of communion with God and as a result of the fact that God has influenced him by His Holy Spirit, trained and changed him. Because the person was influenced and changed by the Holy Spirit – such a person is called spiritual, from the word “spirit”. Since a man is triune and consists of a spirit, a soul and a body, so the influence of God on the spirit of man or the revival of man's spirit produces enormous changes in a one's personality and he or she from a villain turns into a kind and decent person pleasing the Lord.
1 Thessalonians 5:23 And the very God of peace sanctify you wholly; and I pray God your whole spirit and soul and body be preserved blameless unto the coming of our Lord Jesus Christ.