How old is the tree? The Ruby Red was created in FL in 1929; but the Star Ruby was only created in 1970 in Texas.
Other than that, it's probably a difficult differentiation; but IMHO the Star Ruby is the better of the two.

Star Ruby grapefruit is "seedless" (meaning it will have 6 seed or less). The fruit has a large open core area, and the albedo is bright pink, plus the there is a definite strong blushing on the peel. Depending on how old and large your tree is some leaves on the tree will have pale yellow to white patches on them resembling herbicide damage.

Rio Red grapefruit has very red flesh,but the size of the ruit is fairly small.

Johnmerr:
The tree was planted about 2 and 1/2 years ago. It was 6-7 feet tall when planted. About 9-10 feet tall now. Is Ruby Red the same thing as Rio Red? This was the 2nd season for fruit production.
silica:
The fruit has few seeds, definitely less than 6 average. Light pink color to the flesh. The peel is fairly yellow with an occasional blush spot. The largest fruit are4-5 inches in diameter.

Ruby Red and Rio Red are different cultivars. Ruby Red is really "Redblush", and it is truly a "Texas grapefruit", requiring a large number of heat units to develop. You rarely see this cultivar in S. California, although it probably would do well out in the Cochella Valley. I imagine it may do okay in AZ, too, if your growing season is long enough. We here at the coast do not have enough heat units to get Ruby Red to really sweeten up as much as Rio Red will. Rio Red is a sport of Redblush. Here are the links to both cultivars , so you can see if this helps you to ID your tree:

http://users.kymp.net/citruspages/grapefruit.html#redblush
http://users.kymp.net/citruspages/grapefruit.html#riored

Rio Red is probably the only pink or red true grapefruit that has a chance of getting sweet enough for us here at the coast. We actually do better with pummelo/grapefruit hybrids, such as Melogold or Oroblanco, which is what you mainly see in my area, but Rio Red for those that must have something pink colored :-) As in, my husband. I don't like them - too tart for my liking. Love my Oroblancos and Melogolds, though.

Patty S.

Thanks everyone. Patty...the links were great. My vote is Rio Red.