What is the difference between an table index and a view index?

There really is none. The index on both table or view basically serves to speed up searches.

The main thing is: views normally do not have indices. When you add a clustered index to a view, you're basically "materializing" that view into a system-maintained, always automatically updated "pseudo-table" that exists on disk, uses disk space just like a table, and since it's really almost a table already, you can also add additional indices to an indexed view.

So really - between a table and an indexed view, there's little difference - and there's virtually no difference at all between indices on tables and an indexed view.