you can view partners as any kind of business contact, I.e. a supplier or a customer.
User is someone that interacts directly with Odoo. A user can be assigned a partner record (I.e. your Customer can have a User to interact with your database and that user is linked to the partner).
Regarding internal/public/portal user:
An internal user will have full access to the backend system. When you have Odoo Enterprise this type of user will require a license.
A portal user can access the customer portal to see their Sales Orders etc
the public user is someone who visits your Odoo website without authenticating
regards
Also, what's the distinction between Interna User, Portal User and Public User ?