I wasn't a participant in any of this history: just a teenager who read a lot and paid attention to what was happening at the time. I'm also oversimplifying, and I'm probably telling a lot of people things they already know or even things they know better than I do.
Today, when you say the phrase "electronic mail", there's a nearly 100% probability that you are actually talking about Internet Mail: messages in a standard format exchanged using the Simple Mail Transfer Protocol (SMTP). As recently as the 1990s, that statement did not hold true. There was a huge diversity of systems described by the phrase "electronic mail".
One of the first services I used through a modem was CompuServ. I had an account there for a few months, and was it ever expensive. CompuServ had email service. Users could exchange messages among themselves. It was mostly a silo, except for an Internet gateway. If I recall correctly, my CompuServ user ID was `72714.2172`. So I could be reachable from the Internet with the email address `72714.2172@compuserv.com`. There were a few other walled garden online services like CompuServe: GENie, Prodigy, and AOL. I'm fairly certain all of them had mail gateways to the Internet.
Around the same time, I started using local bulletin board systems. Many of these were linked in a store-and-forward network called Fidonet. Essentially, each board in Fidonet peered with other boards. They'd call one another in the wee hours of the morning to exchange electronic mail, files, and echomail. Echomail was basically a many-to-many messaging system. Think Usenet, or forums if the forums were distributed across multiple machines.
Most email sent over Fidonet was between fidonet users, but like CompuServ, there was a gateway from Fidonet to the Internet. When I realized this, the first thing I did was send myself an email message from a local BBS to my CompuServ account. It took days to arrive!
There were dialup services used exclusively for email. For instance, in 1993, you could buy a monthly subscription to ATTMail or MCIMail, and the only thing these two provided was email. According to Wikipedia, MCI Mail also offered "email to snail-mail" service. My fuzzy memory tells me that these services used a protocol called X.400. That was telco stuff, so likely a lot more convoluted than SMTP. At least by the 90s, both services also had an Internet gateway.
Then there was UUCP, another store-and-forward network for exchanging files, electronic mail, and Usenet articles. Initially UUCP was used by Unix machines. I'm pretty sure that by the 90s, there were also PCs running MS DOS on the UUCP network. I used a few MS DOS bulletin boards where the sysop was obviously pulling a UUCP feed. Again, there were gateways from UUCP to the Internet, so that hosts reachable over UUCP could exchange mail with hosts on the Internet.
See the pattern? As late as the 90s, there was this huge diversity of email systems and protocols. Through gateways and radical interoperability, the Internet bridged them. That's how email won. For many people like me, email was the very first Internet service we used, even though we didn't have full Internet access.