I am making a pair of earrings. They go together as a pair but they do not match each other. What word explains this?
From the South China Morning Post, see an article titled 6 asymmetrical jewellery pieces that add edge to classic luxury.
Chanel, Chaumet, Graff, De Grisogono, Harry Winston and Van Cleef & Arpels offer asymmetrical and artistic pieces.
Scroll down to De Grisogono and then to Harry Winston to see two pairs of earrings. Each pair is obviously a pair, but in the De Grisogono pair the role of the diamonds and rubies are reversed, hence the pair is asymmetrical. In the Harry Winston pair, the front and back of each earring can be reversed, so that the lucky owner can wear them as a matching pair or an asymmetrical pair. (Diamonds, sapphires and aquamarines.) The prices are not given: if you have to ask, you can't afford them.
Although the South China Morning Post might seem a strange arbiter of English, in this price range (6 figures and up), fashion writers get it right.
A further option is mix and match (dictionary.com):
(adj) made up of complementary elements taken from different sets or sources
The phrase can also be used as a verb.
It's used in exactly your context: Mix and match earrings: why you should try this jewellery trend (Woman and Home) for example; many shops selling them singly (to allow you to mix and match your own pair) use this term as well.
"Unmatched" conveys the meaning of "not matching" without the connotation of a mistake that "mismatched" has. Although there might be a specific term of art in the jewelry trade as suggested in other answers, an "unmatched set" of anything is clearly two pieces that are not identical.
However, one could also argue that any two pieces of jewelry that are meant to be worn together, but are not identical in color, style, size, and other characteristics, are nevertheless "matched" in the intent of the designer.
I have purchased pairs of non-matching earrings that were listed as asymmetrical, although they were actually similarly proportioned and thus reasonably symmetrical in shape, but their actual designs were different enough to not obviously have been designed as a pair. I think the phrase a 'non-matching pair' conveys both the fact that the two are indeed a pair, and that they were not supposed to be alike.
I would say that they are an odd pair of earrings.
As one of the definitions for odd given in Collins Dictionary:
You say that two things are odd when they do not belong to the same set or pair.
"I'm wearing odd socks today by the way."
I think Randy's answer hits upon it as far as British English is concerned - I would say non-matching, although this is not technically the one worded answer that you are looking for.
There may be a newer, more fashionable term, but this is what would have been said in the past fourty or so years, in the UK. I certainly remember my mother using that expression/term.