A clustered index (SQL Server, MySQL/InnoDB) is a table stored in an index B-Tree structure. There is no second data structure (heap-table) for the table.
A non-clustered index is an index that refers to another data structure containing further table columns.
SQL Server supports clustered index optionally. You have a free
choice between clustered indexes and heap-tables. There can be at most one
clustered index per table. Dropping a clustered index transforms the table
into a heap-table. Adding a
clustered index to a heap table actually drops the heap structure. SQL
Server supports non-unique clustered indexes on arbitrary columns.
Creating an SQL Server table without clustering index requires the use of
CREATE TABLE ( id NUMBER NOT NULL, [...] CONSTRAINT pk PRIMARY KEY NONCLUSTERED (id) )
The MySQL InnoDB engine has mandatory clustered indexes. That means there is always a clustered index, often using the primary key. If there is no suitable unique key available, MySQL will use a generated row ID for that purpose. The MyISAM storage engine doesn't support clustered indexes and uses heap-tables all the time.
The Oracle database has optional clustered indexes called Index-Organized Tables. They work on the primary key only.