Mmm,well,i´m sure about both terms are the same XD.
In letters,78 :
"Urukhai is only a figure of speech. There are no genuine
Uruks, that is folk made bad by the intention of their maker.."
He first refers to the
Uruk-hai,and after he says Uruks.This means that both terms are the same don´t you think?
Even Robert Foster in his book "Complete Guide to
Middle Earth" asumes its equivalence: Uruk-hai = Uruks =
Great Orcs.
In the Appendix is stated that the Uruks make his first aparition in the year 2475,when
Saruman still didn´t have troops,so the conclusion is that the Uruks(Uruk-hai XD) were breed by
Sauron.
In Myths Transformed,it is said that Saruman learned to mix
Men with
Orcs,creating the Half-orcs(Semi-orcs,i´m not sure of the term in english).I´m not telling that Saruman had Uruk-hai in his forces,i just say that is not his invention,but of Sauron.
Maybe you have the reason and in the context they are diferent terms,but i don´t refer to the context but the meaning XD.
Do you understand me?
Greetings.