> For somebody who isn’t super cyprtography-savvy, what’s the difference between over the wire and e2ee?

E2EE: As long as it is correctly set up and no significant breakthroughs happens in math, nobody except the sender, the receiver can read the messages.

> Does the former mean that telegram itself can read non-private-chat messages if it so chooses?

Correct. They say they store messages encrypted and store keys and messages in different jurisdictions, effectively preventing themselves from abusing it or being coerced into giving it away, but this cannot be proven.

If your life depends on it, use Signal, otherwise use the one you prefer and can get your friends to use (preferably not WhatsApp though as it leaks all your connections to Facebook and uploads your data unencrypted to Google for indexing(!) if you enable backups.

Edited to remove ridiculously wrong statement, thanks kind SquishyPanda23 who pointed it out.