A Table Spool operator stores its data in a worktable that is structured as a clustered index. The index is not built on any of the columns in the data, nor on any artificially added columns. It is structured on zero columns. As is normal for a clustered index on a set of columns that is not unique for the set, a 4-byte uniqueifier is then added to the data to give each row a unique internal address.
The worktable for an Index Spool operator is also structured as a clustered index. However, this operator does actually index actual columns from its data instead of just relying on a uniqueifier. The indexed columns are chosen to effectively satisfy the Seek Predicate property. The statement in the Microsoft’s documentation that a nonclustered index is used for Index Seek is not correct.
A stack spool is represented in execution plans as a combination of an Index Spool and a Table Spool, both with the With Stack property present and set to True. This is misleading because it is actually a different type of spool. The worktable it uses is built as a clustered index on a single column, representing the nesting level. Because this is not unique, a uniqueifier is added where needed.
This is a deep look at some operators which people tend to gloss over but can have huge performance impacts.