To what extent are magnets the same as batteries?

The voices in my head are calling magnets ‘batteries’ every time I am thinking of them. I am imagining the vector arrows right now, and trying to understand how magnets (batteries) interact with each other. I only learned a little about this while learning how to use the battery for the electric bike. I learned a little bit about series and parallel. Do the attributes also match, such as voltage, and all that? Are they directly analogous to magnets, but maybe with different names for the units of measurement?

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