For it to be money, it has to be both on some level. But you could imagine a bad currency being better at one than the other.
An example of a terrible store of value but OK medium of exchange might be a currency with predictable but high inflation. Everyone would know their money won’t be worth as much in a few months so we’d all try to spend it quickly on necessities or something that is a store of value. Interest rates would be very high if banks want anyone to save so borrowing costs would be sky high. It’d probably be very hard to run a business.
For the opposite, maybe a situation like Bitcoin where it can gain or lose 30% in a single day. It might be a good store of value over time (or not; we’ll see) but the volatility makes it a pretty lousy medium of exchange. If Bitcoin became the only currency for some reason and stayed just as volatile, merchants would have to constantly adjust prices and consumers would have to constantly keep track. People would probably delay some purchases until the currency went back up and the volatility would make for an unstable economy.
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