In most contexts the two are interchangeable according to Cambridge, Merriam-Webster and Collins. Oxford Languages gives the exact same definition for both terms:
the interaction or cooperation of two or more organizations, substances, or other agents to produce a combined effect greater than the sum of their separate effects.
Collins, however, does make the distinction in Christian theology:
synergism
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- Also called: synergy the working together of two or more drugs, muscles, etc, to produce an effect greater than the sum of their
individual effects
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- another name for synergy (sense 1)
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- Christian theology the doctrine or belief that the human will cooperates with the Holy Spirit and with divine grace, especially in the act of conversion or regeneration
Indeed, while synergism is a position, a doctrine (as opposed to monosynergism), synergy is a countable noun and describes the actual collaboration between the human will and divine grace.
Note that synergy is a countable noun and will take plural regardless of the meaning it is used in, whereas synergism will only take plural when it is used as a synonym of synergy.