A 'partner' is either a person, an association, an organization (company*). * It is better if you don't use company in this definition, as it has another meaning in Odoo.

A 'company' (the way it is more commonly used) is a set of partners (mainly customers, suppliers and employees), users (logins).

An example of a company would be Odoo S.A, Odoo USA or Odoo Asia/Pacific.

A 'customer' is a partner that purchases products from a company.

An 'employee' is a partner that works for a company.

A 'supplier' is a partner that sells products to a company.

Odoo is implemented by people who work for Companies. People are modelled as partners, as are the individuals and organizations that those people buy from, sell to, employ and do business with.