Assign vs delegate

One task that changes hands, or two tasks with a copy.

Both hand work to someone else, but they behave differently. Pick based on who stays responsible.

Assign: one task changes hands

The task changes owner to the assignee. No copy is made: it's a single task.
It lands in the new owner's Inbox to process. The previous owner no longer owns it.
Only works inside a shared project, and only members with access can be assigned.
Optionally tick follow so it shows in your Waiting for as "Following".

You stay responsible; the other person executes.
Your task moves to Waiting for; when they accept, a copy is created in their Inbox.
You track their progress with the status badge and close your own task when done.

Rule of thumb: assign when the other person should own the outcome; delegate when you still own it and are just waiting on them.