Kendra Little explains the two types of filtered indexes:
These two filtered indexes are very different – and the SQL Server optimizer can use them very differently!
While classic filtered nonclustered rowstore indexes must reliably “cover” parts of the query to be used to the optimizer, filtered nonclustered columnstore indexes may be combined with other indexes to produce a plan returning a larger range of data.
This sounds a little weird. I’ll show you what I mean using the WideWorldImporters database.
Kendra exposes an interesting difference in the two types of index and a case where filtered indexes simply fail (though that’s not a situation you want to be in anyhow!).