My orange tree is now about 3-4 years old. When I bought it, it was grafted with another type of orange tree. This year is the 1st year that it is producing fruit but only on the side without the thorns. I was told to cut the thorn one down because it will not produce fruit and it is stealing nutrition from the producing side.
I assume you had a branch start to grow up from the root stock, the one you mention that has thorns.
Most citrus root stock used for grafting has thorns. It should be able to be pruned away, but you should not do this until the tree is dormant.