You're right to be confused, and irritated. Yes, they're synonyms. I don't know who decides or how they decide which one is primary and which is a no-longer-accepted synonym. Some plants have synonyms because there was prior confusion about juvenile/mature leaves so were thought to be different species, and some because genetic testing reclassifies the plant, though binomial nomenclature has never been about genetics until very recently. Some species names translate from Latin to English to mean something like "hairy, red, has big flowers," or are even made-up words partially including someone's name, or the region in which they were discovered.
Species names are often repeated. To properly indicate a plant, both genus and species name are required. For example, zebrina. There's Malva zebrina and Tradescantia zebrina.
