In IRC terminology that was a "network", not a "server"; multiple servers worked together as part of a network (which might have only had a single server in the degenerate case) to create a unified channel namespace and it didn't matter which server you used (and yes, I know that at some point server-local channels were added as a thing using ##, but despite using IRC for a quarter of a century I never once saw anyone use them except to be weird). The term "server" used in the way Discord decided to use it is awkward and even off-putting.
In TS/Mumble/Vent terminology, there was no federation (unlike IRC), so a server was generally literally a single server hosted somewhere. All the channels, all the users, etc, went to a single machine.
Discord's selling point isn't really being a "better IRC", it's the voice chat. It's a better TS/Mumble/Ventrillo. Low-latency, decent audio quality, push-to-talk or an actually functioning level detection, with an easy to use interface. It's "Chat for Gamers" for a reason, not "IRC with history".
True, but you had to pay for a server for TS/Vent/Mumble as well, so the $5/month Discord charges for the higher voice quality is comparable (or cheaper).
Discord is voice chat, with text as a nice extra, and with image/file sharing and screen sharing and emoji/stickers/profiles (these are attractive to some people). IRC is text only. TS/Mumble/Vent were all voice chat, with really awful text chat interfaces (TS was sort of OK, Vent may as well not have had text chat).
I don't think Discord is good as an information archive, and I'm not terribly fond of seeing FOSS projects using it as a primary means of communication, but it's great for gaming compared to what we had before.
FWIW a bunch of people do seem to agree (though that isn't to say a bunch of people disagree). Maybe it is because I'm "old and set in my ways". Maybe it is because I'm just too familiar with IRC (while having never used TS nor even heard of the other two). Or maybe it is because I actually run servers for things (including IRC). But every time I hear "my Discord server" a very large part of my brain gets confused: it is a word which is so incorrectly-to-me being used--being neither a literal nor a metaphorical (via IRC) description of what is going on--that it causes me momentary confusion and then even a twinge of anger that this is what "server" means to people in 2022: a mere account on a service that isn't even themselves running a server for the user :(.
It's modeled off of IRC / Mumble / TS / Vent terminology. A server is home to many channels which one can join.