The OED defines galvanism (coined ~1792) as
Electricity developed by chemical action
and voltaic (coined ~1813) as
Used in producing electricity by chemical action after the method discovered by Volta
and
Of electricity: Generated by chemical action.
Are "galvanic" and "voltaic" synonyms?
Not really, although they broadly referred to the same phenomena. Galvanism was associated with a particular view that ascribed special powers to living organisms in producing "animal electricity". Some, although not Galvani himself, even thought that there was a special "galvanic fluid" separate from electric fluid, perhaps an embodiment of élan vital. Volta attempted to dissociate "galvanic" from that context, and for a while "galvanic electricity" was treated as a special phenomenon whose nature was to be established.
Oersted delivered lectures on Electricity, Galvanism, and Magnetism in 1819-20, Ampére named a measuring device "galvanometer" in 1823, and Ohm titled his seminal paper Maassbestimmungen über die Galvanische Kette (Measurements of the Galvanic Circuit). After the acceptance of Ohm's theory the name persisted mostly in popular literature and Naturphilosophie standing for a "force of nature", like gravity but more animalistic. Mary Shelley's Frankenstein, Schelling, Hegel and Schopenhauer ("galvanism overcomes chemical affinity... and so entirely suspends the laws of chemistry"), among others, mentioned Galvanism, see How influential was “galvanism” on philosophy?
In contrast, there was no "Voltaism", after Volta's demystification of "animal electricity" it was gradually absorbed into electrochemistry, with major contrinutions from Ampére and Ohm, see What is the history of electric current and resistance? "Voltaic" referred to electricity generated by voltaic piles and similar processes. A good idea of the use of both terms can be gotten from e.g. Whittaker's classic History Of The Theories Of Aether And Electricity, ch. III, From Galvanism to Electrodynamics by Caneva and The Electric Current in Early Nineteenth-Century French Physic by Brown:
"Although there were few, if any, relevant papers in the French journals in the 1780's, by the 1790's members of the Institut had started to consider the multiplying and perplexing phenomena of "le Galvanisme." Reports on new aspects of "l'influence de l'application des metaux sur l'irritabilité et la sensibilité" were frequent in 1796 and 1797, and during 1798 a regularly functioning "Commission du Galvanisme" consistently reported new discoveries and experiments. By 1800, the variations and complexities of galvanic irritability were still pursued as popular and respectable research topics.
But in 1800 the discussion of "animal electricity" entered a new phase in France as in the rest of Europe. Volta, a professor of physics who had been supporting a rival theory to Galvani's since 1792, announced his invention of a device, the "pile," with which he claimed to overthrow once and for all the theory of the "animal electricians"... All that the animal electricians really see in their so-called "galvanic" phenomena, he argued, are the physiological effects of contact-induced and pile-multiplied "voltaic" current."
