Crypto would represent more of a money in such an example, as crypto wouldn't be the end goal of either party, merely a means of transaction.
Barter is more primitive, and has the problem of double-coincidence of wants. For example, I'm a chicken farmer and I need milk, so I have to find a guy that both HAS milk and WANTS eggs. Then, he can gouge me if I'm desperate (or vice versa), because it's hard to find another in that situation.
Crypto, by preventing us from ending up in that situation, avoids barter by becoming money itself.