Yes, Manifold Enterprise can store geometry in a database (you get your choice - you're limited with ESRI to an MS Access for personal geodatabases). This works the same, generally, as Oracle spatial or ESRI's geodatabase. With ESRI's geodatabase AND ArcSDE, you can perform simultaneous editing - that is two people can edit the same drawing at the same time. This can get very complicated when you go to put the edits back together etc. Manifold, I feel, has a much slicker way of doing this.

In Manifold, yes, multiple people can be linked and view a particular component at the same time. Here's the difference - first, only one person can edit something at a time. They effectively "sign it out". This is similar to ESRI's personal geo-database; but here's the difference. When you are linked to a component in Manifold, there is a little grey "lock" beside it. When someone "signs a component out", the lock turns red, and if you hover over the component, you can see who on what machine has signed out the component. You will even be notified if your cached version of the component (you can choose not to cache) is out of date. There are other features too of this - to numerous to go into in detail. We (where I work) did a bit of an evaluation between ArcSDE and Manifold Enterprise, and haven't found anything to justify the price of SDE. Hope this helps.