That's not a difference in what they do or even in how they're used. There are plenty of subreddits that rely on real-time interaction between posters; arranging pokemon trades is an obvious example.
If I make a comment in a large Discord server, and then put my phone back in my pocket and continue my day, I am very unlikely to actually see any responses to what I said.
Discord will alert you to their existence, highlight them for you, navigate you straight to them, and jump you back to your original comment so you can read forward from there. That last option doesn't even require your responses to be marked as responses to you.
If you don't see the responses, that's because you didn't want to.
But "Read forward from there" is often just way too much text, with no clear delineation between different topics other than reading it. Reddit encapsulates topics into their own spaces that can live outside of an ever-increasingly long scrolling text screen.
I regularly get so far behind on channels in an 11 person server that I just give up on reading whatever I missed that day. If Discord and Reddit can serve functionally identical purposes in your life, that's fine, but to deny that they have any functional differences to anyone is just provably false.
The difference is purely branding.