For DROP and TRUNCATE, no difference because the only things need to be updated are global/global partitioned indexes. But for other operations, there is a difference
SQL> create table t (x int, y int, z int )
2 partition by range (x)
3 (
4 partition p1 values less than (4000),
5 partition p2 values less than (8000)
6 );
Table created.
SQL>
SQL> insert into t select q*1000,rownum,rownum from dba_objects, ( select rownum q from dual connect by level <= 7 );
604877 rows created.
SQL> commit;
Commit complete.
SQL>
SQL> create index ix_local on t ( y ) local;
Index created.
SQL> create index ix_global on t ( z ) ;
Index created.
SQL>
SQL> alter table t split partition p2 at (6000)
2 into ( partition p2a, partition p2b )
3 update global indexes;
Table altered.
SQL>
SQL> select index_name, partition_name, status
2 from user_ind_partitions
3 where index_name like 'IX%';
INDEX_NAME PARTITION_NAME STATUS
------------------------------ ------------------------------ --------
IX_LOCAL P1 USABLE
IX_LOCAL P2A UNUSABLE
IX_LOCAL P2B UNUSABLE
3 rows selected.
SQL>
SQL> select index_name, status
2 from user_indexes
3 where index_name like 'IX%';
INDEX_NAME STATUS
------------------------------ --------
IX_GLOBAL VALID
IX_LOCAL N/A
2 rows selected.
SQL>
SQL> alter index ix_local rebuild partition P2A;
Index altered.
SQL> alter index ix_local rebuild partition P2B;
Index altered.
SQL>
SQL> alter table t split partition p1 at (2000)
2 into ( partition p1a, partition p1b )
3 update indexes;
Table altered.
SQL>
SQL> select index_name, partition_name, status
2 from user_ind_partitions
3 where index_name like 'IX%';
INDEX_NAME PARTITION_NAME STATUS
------------------------------ ------------------------------ --------
IX_LOCAL P1A USABLE
IX_LOCAL P1B USABLE
IX_LOCAL P2A USABLE
IX_LOCAL P2B USABLE
4 rows selected.
SQL>
SQL> select index_name, status
2 from user_indexes
3 where index_name like 'IX%';
INDEX_NAME STATUS
------------------------------ --------
IX_LOCAL N/A
IX_GLOBAL VALID
2 rows selected.
SQL>
SQL> alter table t drop partition p1a update indexes;
Table altered.
SQL>
SQL> select index_name, partition_name, status
2 from user_ind_partitions
3 where index_name like 'IX%';
INDEX_NAME PARTITION_NAME STATUS
------------------------------ ------------------------------ --------
IX_LOCAL P1B USABLE
IX_LOCAL P2A USABLE
IX_LOCAL P2B USABLE
3 rows selected.
SQL>
SQL> select index_name, status
2 from user_indexes
3 where index_name like 'IX%';
INDEX_NAME STATUS
------------------------------ --------
IX_LOCAL N/A
IX_GLOBAL VALID
2 rows selected.
SQL>
SQL> alter table t drop partition p2a update global indexes;
Table altered.
SQL>
SQL> select index_name, partition_name, status
2 from user_ind_partitions
3 where index_name like 'IX%';
INDEX_NAME PARTITION_NAME STATUS
------------------------------ ------------------------------ --------
IX_LOCAL P1B USABLE
IX_LOCAL P2B USABLE
2 rows selected.
SQL>
SQL> select index_name, status
2 from user_indexes
3 where index_name like 'IX%';
INDEX_NAME STATUS
------------------------------ --------
IX_LOCAL N/A
IX_GLOBAL VALID
2 rows selected.
SQL>
SQL>