Wikipedia currently treats them as synonyms (redirecting "retrowave" to synthwave) and I couldn't find any authoritative sources, but according to user Zsokorad on Reddit:
Synthwave is the all-encompassing genre of "music with synthesizer sounds". Synthwave started in the late 70s and has been around ever since to some degree. But there have been two points where the popularity soared: the 80s and...well...right now. The boom period in the 80s is just known as Synthwave, as that is where it became a thing, while what is going on right now is Retrowave.
Retrowave is a sub-genre of Synthwave that is all about mimicking the styles made popular in the original 80s boom period. Retrowave has several sub-sub-genres under its umbrella, each focusing on one of those mimicked styles. The best way that I can separate them is by describing a scene and letting you imagine the soundtrack for it.
So, if we take this as definitive, synthwave is the original synthesizer-heavy music style popular in the 80s, and retrowave is the modern imitation of that music --the synthwave revival. As with any revival, the similarities are a lot of the point, but there's always a difference between how it was done originally, and how it is reinterpreted by new musicians.
