State-of-the-art means: "the latest and most sophisticated or advanced stage of a technology, art, or science."
So where state-of-the-art relates to technology, it is a subset; therefore they are not synonyms.
In case you're not sure of the word technology, it means: "the branch of knowledge that deals with the creation and use of technical means and their interrelation with life, society, and the environment, drawing upon such subjects as industrial arts, engineering, applied science, and pure science."
As to what technology means in Greek, Etymonline.com can tell us that:
1610s, "discourse or treatise on an art or the arts," from Gk. tekhnologia "systematic treatment of an art, craft, or technique," originally referring to grammar, from tekhno- (see techno-) + -logia (see -logy). The meaning "science of the mechanical and industrial arts" is first recorded 1859. High technology attested from 1964; short form high-tech is from 1972.
Further discourse from me on the etymological nuances of the words would be unnecessary, since Colin Fine has now provided an excellent few paragraphs on the subject.