I don't recall the first all-electronic email I sent, but odds are it was via CompuServe (to another CompuServe user). Another service allowed sending a message pseudo-electronically. The idea was simple: address the e-mail just like a piece of snail mail, and then [send]. It would be printed near the destination, and enter the standard US Mail system, arriving in the destination mailbox like any other letter (I recall an optional signature, which you invoked by keying /*SIGNATURE*/ at the appropriate place). I'm sure services like that still exist, but I haven't used one in over 20 years.
I can still remember my "72265,23" CompuServe login! Eventually, they began experimenting in sending messages to other networks, but I recall them being very slow to introduce it, which is why I signed on with another service. I even remember buying an O'Reilly book which explained how to send messages from one network to another, using the various gateways that popped up. Remember: these were the early days of The Internet!
Do you remember "bang addressing"? ("bang" is slang for "!") Then, you had to know the route that email would take to arrive at a destination, so something like dallas!denver!boulder!cu!genebob was required (and that wouldn't work for your friend in New York). Eventually, the well-known services migrated to @ addressing which we know today.
queue Time Machine: I played with Prodigy software for awhile; this was PC application software which understood a vector graphics language called NAPLPS and was much cooler than the text-based CompuServe. NAPLPS could send commands like "draw a red circle of radius 30 at coordinates 100,150" (in the days of 300/1200 bps dialup modems, that was much more efficient than transmitting a bitmap).In a way, NAPLPS reminds me of another language at that time, called LOGO which was used on Texas Instruments' 99/4A microcomputer (I briefly used those in 1983, not long after the IBM PC debut of 1981).
Hmm .. these memories will undoubtedly refresh brain cells that haven't activated in a lonnnnnnnng time. Time for an RC and a Moon Pie ...
Reference: H@ppy birthday to you (BBC)