The "Public User" is a user who isn't logged in. Odoo utilizes the access rights of this 'fake user' on your website for visitors who aren't logged in. Essentially, you shouldn't create a public user unless you're dealing with complex installations or configurations, such as a multi-website setup with multiple companies.

A "Portal User" is a customer who has access to the portal (/my/xxx) to view their own documents.

An "Internal User" is an "employee" or privileged user who will have access to the backend (/web) and more information than just their own.