That's only half true. Yes, Discord does allow a "rich" chat experience, with channels and servers, but there the similarities end.
IRC is based on an open protocol, with many open source clients available for it, and a decentralized server infrastructure.
Discord is closed and centralized, with only a single client available for it.
You can easily log IRC channels, but there is no easy way to do that on Discord, if it can be done at all.
I've logged every channel I've ever visited on IRC, and I can use powerful text tools to regex search through all of my conversations on IRC and have the results appear instantly. Nothing remotely like that is possible with Discord.
Paging through IRC logs is virtually instant on a modern terminal, while Discord makes you wait a long time between every other page load, so if you need to look through more than a handful of pages it's incredibly slow and painful.
Some IRC channels have their logs published on the web, making them fully searchable through web search engines, but to my knowledge no Discord channels do that.
What happens in Discord stays in Discord.