The difference is the Holy Spirit. The spirit in 2:7 is human spirit, not the Holy Spirit. Actually it's not just human spirit, but life sustaining spirit, any animal that breathes is endowed with it.
Then just consider them left brain and right brain, the conscious and the subconscious, alright? "Soul" means "living being", "spirit" means "breath", without breath you'd be dead, you'd cease to be living, see Lk. 23:46 - "When Jesus had cried out with a loud voice, He said, “Father, ‘into Your hands I commit My spirit! ” Having said this, He breathed His last."