Hi Andrea,
MediaSpace is a not free software, it only has a commercial version.
You can host it on your own ENV or use it as SaaS from Kaltura's DC but either way, it costs money.
CE is completely free and is licensed as AGPLv3. It is basically the free edition of the Kaltura Server, which is the same code base that is used for running our SaaS at kaltura.com.
MediaSpace makes API calls to the Kaltura server to achieve its operations so, if you choose to go with CE, you will need implement your own front end for it, like MediaSpace does.
CE does include management consoles such as Admin Console and KMC but these interfaces are meant for the people who administer the platform, not for end users.