"Omeka.net is a lite-version that does not require its own server. "
If you do not have access to a server, you can register for an Omeka.net account to get started.
The Omeka full-version is downloaded via Omeka.org and installed in your server."
To use Omeka.org, you must have access to your own server.
Omeka.net (hosted): Some organizations and individuals couldn’t or didn’t want to run their own server or buy commercial server space. Omeka.net is a hosted version of Omeka that requires much less technical knowledge, infrastructure, and labor. When you use the hosted version of Omeka at omeka.net, it’s much easier, but you will run up against certain limits of space and functionality (French, 2013). Omeka.net offers 5 different hosted plans to choose from. You must sign up for a free account to be a user/collaborator on any Omeka.net website. See here for more information on Omeka.net options and pricing.
Omeka.org (self-hosted): The Omeka web publishing software is available for free download. The free, open source version can be self-hosted on a web hosting server or your personal PC if a virtual server program is installed (i.e. MAMP). Commercial web hosting is also available, for more informaiton review Omeka’s hosting suggestions. When you download and self-host Omeka, you can customize it as much as you want and install it as many times as you like, but creating and supporting those Omeka sites may take a good bit of knowledge and time. (French, 2013). For step-by-step instructions and video tutorials, visit Omeka Documenation.