According to the Artscroll Selichot in the introduction, a שלמונית is "a piyut composed exclusively of quatrains, or four-lined stanzas."
This definition fits most of the selichot, maybe 75%, but most of them are not labeled שלמונית. In some cases this is because the selicha has another designation, like פזמון or פתיחה, which takes priority, but many times it has no label at all. The first example is selicha #2, אין מי יקרא בצדק.
Why are some of them labeled שלמונית and some aren't?
I cannot verify the source of Artscroll's definition. Upon inspection, it appears that a שלמונית is a four stanza סליחה, specifically in which every stanza ends with a fragment of a פסוק. In many cases, the first word and the last word of each stanza are the same. #30-33 all fit this description; 37, 38, 51 do not end and begin with the same word, but each stanza ends with a פסוק fragment (with the exception of the first stanza of 38). In #64, each stanza begins the same way but doesn't end the same way, though they do end in פסוקים fragments. 73 follows the previous description of the repeating words and פסוקים fragments. (For some reason unknown to me, days 4 and 5 of עשרת ימי תשובה don't have a שלמונית.)
