Odoo community versus Odoo enterprise
Odoo is the name of the software product, and also the name of the company that builds it. Odoo follows an open core business model, where the community edition (CE) is free and open source, and the enterprise edition (EE) is a paid product, providing income for the company.
The CE provides all the framework features plus the essential features for most of the business applications bundled with Odoo. It is licensed under an LGPL license, chosen to allow adding proprietary extensions on top of open source modules.
The EE is built on top of the CE, providing all its features plus some additional exclusive ones. Notably, it includes an improved and mobile-friendly user interface, although the user interface underlying the organization is essentially the same in both editions.
The Odoo online SaaS service uses Odoo enterprise, and may have deployed intermediate versions released after the latest Odoo enterprise major version.