Personal Inbox
Your personal Inbox is a default project, which only you have access to. You can easily and quickly add tasks there if you’re on the go and move them to other projects later.
Your personal Inbox can't be shared with other users (whether they’re on your Business plan or not) and it can’t be deleted.
Team Inbox
Your Team Inbox is a default shared project that every user on your Business plan has access to. Whenever your team has a task that doesn’t belong to a particular project yet, it can be added to your Team Inbox. Everyone on the team will be able to see it, as well as edit or complete the task.
The Team Inbox can’t be shared with people that aren't on your Business plan, and it can’t be deleted unless you cancel your Todoist Business account.
Because your Team Inbox is shared with your team, you can assign tasks to team members in your Team Inbox.