It occurred to me yesterday that I know two Latin words for rain: pluvia and imber. However, I don't seem to know how these two words compare to each other, and the L&S entries offer little help. Are they essentially synonymous, or are there differences I should be aware of?
Yes, there is a technical difference, though the meanings tend to shade one into the other.
Roughly, pluvia is the wet stuff itself, the falling water that comprises the shower, imber.
More or less as you would in English, it's quite legitimate to use either, as you wish, to describe the actual weather. Imber, however, does tend to mean heavy or cold rain, rather than a gentle, soft shower. An example that comes to mind is the description of the weather on the day of Galba's downfall (Tac. Hist. 1, 18):
Quartum idus Ianuarias, foedum imbribus diem, tonitrua et fulgura et caelestes minae ultra solitum turbaverunt.
But if you were translating Portia's plea from the Merchant of Venice, where 'the quality of mercy . . . . . droppeth like the gentle rain from heaven', pluvia — the rain water itself — would be the word to use.