Slack has basically one main hierarchy level (messages are grouped into channels) while Zulip has two, streams and topics. So you can create a stream for each project (say) and create a different topic for any given point that needs discussion about that project.
Kind of like if each slack thread discussion had a title and was discoverable from the left sidebar and didn’t get in the way of the other threads.
But also, critically, if you want to, you can drop back to the "show me everything sequentially" view. Threads hide discussions away - which is good when you want to focus on something else, but bad when you can't remember where a discussion was.
From what I have read (not having actually used Zulip) it always sounded like the chats were threaded in the same way that mailing lists or newsgroups are threaded.
Kind of like if each slack thread discussion had a title and was discoverable from the left sidebar and didn’t get in the way of the other threads.