Rad and Gray are absorbed dose units. When we look at radiation being absorbed in tissue, the absorption
varies with the energy of the radiation. With a higher energy deposition in tissue, there are more rads or more Grays deposited than a lower energy deposition at the same rate (particles or photons per second).
Now, what is a rem and what is a a Sievert? The term rem came from an acronym that means Roentgen Equivalent Man, in another words the equivalent biological damage done to human tissue. Some radiation emissions, when depositing the same energy as other radiation emissions,
do more biological damage to the human organism than others. How does one convert?
To go from rad to rem or from Gray to Sievert, you need a multiplication factor that represents the effective biological damage. Most training texts call this a quality factor (QF) or a radiation weighting factor. Some training texts call it a biological damage conversion factor but what it truly represents is the the ratio of biological damage done by radiation types to the biological damage done by gamma radiation.
For gamma, x-ray and beta radiation, this factor is 1. For alpha, it is 20. For neutrons it is between 3 and 10, and is generally conservatively taken as 10. What this implies is that a rad or Gray of alpha energy absorbed by soft human tissue does 20 times more damage than a rad or Gray of gamma, x-ray or beta energy absorbed.
Since for gamma, x-ray and beta, the multiplication factor is 1, one rad equals one rem and one Gray equals one Sievert. There is an excellent video animation on this subject
by Ionactive Consulting of the United Kingdom on their website. View the video
if you want a more detailed explanation these concepts.