OK, so latin botanical names have synonyms? How confusing! Sorry I was of no help. The plant in your photo...is it current? It is quite strikingly beautiful.
They certainly do! From what I've gathered, this seems to happen when two people 'independently discover' the same plant and proceed to each give it their own name and also when taxonomists decide that this plant (or these plants) are actually more clsely related to these and belong in this other family/genus et c. A good example of this is that all plants formerly known as Coleus (which was the old genus name) are now in the genus Solenostemon. Many of them actually kept the same species name while switching over to the new genus, but sometimes plants are renamed completely.