Hi,

1. Odoo Studio and Accounting Module in Community Edition:

• Odoo Studio: Odoo Studio is available only for the Enterprise edition. However, in the Community edition, you can customize and create new modules as per your need. This requires some technical skills​.
  
• Accounting Module: Many features are not available for the Odoo Community Edition accounting module. But these features can be enabled in the community edition version. For this, you need to set up a group for your users in settings​. That group comes automatically after installing the invoicing module in Community Edition. The group name is "Show Full Accounting Features". After setting up your user under the group, you get some features of the accounting module that are not available in the community version​.

   2. Differences between Odoo Deployments:

• Odoo Online: This is a SaaS (Software as a Service) based system. Your cloud instance will be ready to use anywhere and at any time in a matter of seconds and a couple of clicks. It even comes with a pre-configured email server. Odoo supervises the platform for optimal performance, and the 24 hours team ensures that the cloud platform scales as your business grows.
  
• Odoo.sh: This is a PaaS (Platform as a Service) rendered and managed by Odoo SA. It allows the users to deploy their own Odoo cloud platform. It is made for customized Odoo implementations. You can easily install certified apps as well as any third-party apps available on the Odoo apps store.
  
• Odoo On-Premise: This involves installing the software on a company’s own servers. This gives businesses more control over their data and infrastructure, as well as the ability to customize the software to fit their specific needs. However, Odoo SA cannot provide any guarantee or Service Level Agreement regarding the robustness, performance, and scalability of your infrastructure.

The Community Edition can be deployed on-premise. It is a free and open-source version of Odoo with fewer features and customization options compared to the Enterprise edition. The On-Premise deployment refers to the method of deployment, not the edition of the software. So, you can have an on-premise deployment of either the Community or Enterprise edition.

Hope it helps.