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 in your Business team or not) and it can’t be deleted.
Your Team Inbox is a default project that every Business team has. Whenever your team has a task that doesn’t belong to a particular project yet, it can be added to your Team Inbox. Everyone in 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 outside your Business team, and it can’t be deleted unless you cancel your Todoist Business account.