Quite a lot, actually. The two really don't have anything at all in common. Zimbra is a full Microsoft Exchange replacement while ActiveCollab is just for project management.
In addition to the calendars and collaboration stuff, it's also a complete mail system, which is why you won't see it as a user-installable option at any web host. If you want to run Zimbra, you'll need a company that offers Zimbra virtual hosting or get a dedicated server.
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