To which distinctions does the term "hymenoptera" refer?
I don't have a definitive answer, but I suspect Hymenoptera is "just a name," albeit a name that has lasted through the phylogenetic nomenclature revolution.

Hymenoptera was erected by Linnaeus in the 10th edition of Systema Naturae (1758). The description of Hymenoptera (membrane wing; p. 553 [hope your Latin is better than mine]) follows that of Lepidoptera (scale wing) and Neuroptera (net wing) and precedes Diptera (two wing). 

Classical taxonomy, which Linnaeus was more or less inventing at the time, was based on shared similarities. Those insects which Linnaeus thought more similar to each other than to other insects (e.g., ants, wasps, bees) all shared the characteristic of having a membrane based wing. The scaly wings of moths and butterflies made them more similar to each other.

He needed names for these groups, so he chose logical ones based on outward appearance of the wings: scaly, netted, membranous, or paired. That fact that these major groupings have more or less stood the test of time suggests that Linnaeus picked a good characteristic on which to name his classification of the major groups of insects.