Sharing a list with a user will duplicate the list on the user's Google Account and sync all the changes between your two lists.
At least one of the users on the shared list will have to go on TasksBoard in order to sync the list as this is not a feature natively supported by Google Tasks.
To share a list of tasks please open the three dots menu of the list you want to share then click on "Share list".
You will get a sharing link that you will be able to send to your collaborators so that they can join the list.
Your collaborator will then have to open the link and accept to share the list with you before you can share the list and assign tasks to them.