First of all I have to mention that I developed Tizen projects only for Tizen Wearable, so I can't tell you anything about Mobile/Tv programs.
But I can tell you that:
1 - Web and native projects are not the same (you can't do background service in web projects)
2 - there are some similar functions in web and native but they CAN work not in the same way.
3 - If you have custom UI - it is better to make it in web app, but if you need to use some native Tizen functions (such as access to contacts, services, etc) - you should use native app.
4 - you can create a hybrid app (that is very important when you have custom UI and need access to native TIZEN services)
Can they all provide the same functionality?
NO
There are currently 3 ways to develop a wearable application
NO, you can't use C# on wearable (since 3.0 is a last version of tizen wearable and C# needs Tizen 4.0)