Four statements look after a table's physical storage, and InnoDB changes what three of them do:
ANALYZE TABLE orders;
OPTIMIZE TABLE orders\G+-------------+---------+----------+----------+
| Table | Op | Msg_type | Msg_text |
+-------------+---------+----------+----------+
| shop.orders | analyze | status | OK |
+-------------+---------+----------+----------+
*************************** 1. row ***************************
Table: shop.orders
Op: optimize
Msg_type: note
Msg_text: Table does not support optimize, doing recreate + analyze instead
...ANALYZE TABLE re-samples index statistics cheaply; UPDATE HISTOGRAM ON col builds a histogram (Index Statistics).
CHECK TABLE verifies pages and indexes; its MEDIUM, EXTENDED and CHANGED options apply only to MyISAM. CHECKSUM TABLE hashes the contents, which proves a restore (Logical Backups).
OPTIMIZE TABLE on InnoDB means ALTER TABLE ... FORCE, an online rebuild that reclaims the space of deleted rows (a second row reports OK). Keep it for tables that lost many rows.
REPAIR TABLE serves MyISAM, ARCHIVE and CSV only; on orders it answers "The storage engine for the table doesn't support repair". InnoDB corruption means restoring a backup.
mysqlcheck --analyze --all-databases runs them from cron (Cron, Logs and journalctl).