I used to wrestle with distinguishing between these degrees of the spirit and how they were conferred - especially when I read the account of the faithful Cornelius in Acts 10. How was it the that the gift of the Holy Ghost was poured out upon these gentiles before baptism? A sign that God was no "respecter of persons" and that the gentile grafting into the mother tree was underway. Peter, a devout Jew was initially astonished at this even after God had prepared his heart to understand through a heavenly vision and other infallible proofs.
I wondered how this could be in light of other scriptures about the requirement of baptism befor the conferral of such gifts. I always chalked it up as the exception to the gospel pattern. Then I came across a sermon given by Joseph Smith in 1842, where he explained:
I've seen many debate that there is a difference between the phrases Holy Ghost vs Holy Spirit even though they are used interchangably in many instances as they have grappled with these finer distinctions.
You may want to peruse, "Joseph Smith's Doctrine of the Holy Spirit Contrasted with Cartwright, Campbell, Hodge, and Finney" by Lynne Wilson of Marquett University.
A pretty comprehensive study.