The clustered index is the logical ordering of the data of the table itself into a B-Tree structure. Without a clustered index, the table itself is then stored in a Heap data structure, logically. This article, Clustered Index vs Heap in SQL Server, goes into the structural differences between the two.
One other thing to note is the clustered index also specifies a deliberate ordering to the data, when logically stored, whereas a table without a clustered index, and therefore logically stored as a Heap, will typically have no order and therefore is randomly sorted logically.
The benefits of utilizing a clustered index on a table, when architected properly, is that it can be used to improve performance of queries that it covers when the SQL Engine can seek on it for the predicates of those queries, as opposed to a table without a clustered index that would end up requiring a full scan.
To your question regarding the differences between a clustered index and nonclustered index: the clustered index sorts the table itself, logically, the nonclustered index sorts a copy of the data (whatever fields that nonclustered index covers and includes) from the table, logically.
Regardless of whichever logical data structure that is used, physically the data is stored in Pages and Extents on disk. Pages are typically sets of 8 KB of data, whereas Extents are a collection of 8 physically contiguous Pages.