I wonder what the difference is if someone with the priesthood prays for someone who is sick and they get healed compared to a preacher in another church who prays for the sick who gets healed.
That is a great question. It seems that there are certain categories of healings that all have the common roots of faith and/or God’s will. Faith and God’s will transcend any or no organized religion. This means that people can be healed through the prayer of faith regardless of their or the preacher’s membership in a particular church. Prayer is certainly one way that healing power can be brought to bear on someone who is ill. James 5:16 says:
“Confess your faults one to another, and pray one for another, that ye may be healed. The effectual prayer of a righteous man [or woman] availeth much.”
Another category of healing is fasting. When a group of people show their faith and love through fasting and prayer, more power is brought to the healing process.
Still another category in healing is priesthood blessings. A worthy priesthood holder has authority and power delegated to him from The Lord Jesus Christ. Such a holder of the priesthood can call down power from heaven in behalf of the afflicted and heal them completely according to their faith, the faith of the afflicted and God’s will. For a thorough discussion of priesthood blessings, you can read or watch Elder Dallin H. Oaks’ talk from the April 2010 General Conference.
The shorter answer is that all of these ways work to heal, but if I couldn’t have all three at once, I would opt for the priesthood blessing as the most efficacious of the three.”