By request we have this analysis.
Consort comes from the Latin "con" for "with or through" and "sors" for "lot" as status or class, with some Indo-European roots in "sers" for the same. Then through the French "consort" to Middle English, it came to mean "to associate" and then the noun as of one who associates with another. It is now used predominantly to describe a spouse of a monarch.
Meanwhile, valet is a Old French derivative, c. 1560, of vassal which is a Middle Latin derivative ("vassallus"), c. 1300, of the Welsh "gwas" for "a young man" and Celtic/Irish "foss" for "servant". Of course, vassal still retains the meaning of a servant (a squire or a page to a nobleman), but c. 1600 came to be used exclusively with one who was tied to the land from the Feudal system. It's an interesting bifurcation of the word, needing one for the man and the land (vassal), and one for the man and the person (valet) generally inside the home. Today, valet is typically used for someone who takes care of clothing or your car. Odd division of labor, but both functions are still relative to the personal property of the "lord", and now the "lady".
Now the interesting comparison is that valet in the technical etymological sense would accompany the noble, much as the consort in the literal etymological meaning would, however, a consort had no particular gender associated with the position, and was frequently applied to women (that the reigning monarch was almost always a man until modern times), whereas a valet was only a manservant to a gentleman. There is also an inherent usage with consort that the individual is not a servant, although not an equal, but more of a companion. We can make all kinds of disparaging observations about the role of women relative to men in society, but there is no reason to give such a companion a different title when the word servant (or it's equivalent) already exists if his/her sole function were just as a servant.
That said, these words have fairly limited and specific usages. When I arrive at the hotel, I send my dress to the hotel valet to be pressed before the concert. Her husband has often extolled the virtues of having a personal valet, but the best she did was send his shirt out to be laundered. Since watching Ferris' Bueller's Day Off, I don't like having my car parked by the valet--never know what they do with it while I'm having dinner. Boring. After the Trojan War, the women of Troy were apportioned to the victorious Greeks as consorts (some may say concubines, but we'll deal with that word later). Prince Philip is the consort of Queen Elizabeth. Ok, you get the picture. The unequal spouse.