The main differences between InnoDB and MyISAM ("with respect to designing a table or database" you asked about) are support for "referential integrity" and "transactions".

MyISAM:

1. MyISAM supports Table-level Locking
2. MyISAM designed for need of speed
3. MyISAM does not support foreign keys hence we call MySQL with MyISAM is DBMS
4. MyISAM stores its tables, data and indexes in disk space using separate three different files. (tablename.FRM, tablename.MYD, tablename.MYI)
5. MyISAM not supports transaction. You cannot commit and rollback with MYISAM. Once you issue a command it’s done.
6. MyISAM supports full text search
7. You can use MyISAM, if the table is more static with lots of select and less update and delete.

InnoDB:

1. InnoDB supports Row-level Locking
2. InnoDB designed for maximum performance when processing high volume of data
3. InnoDB support foreign keys hence we call MySQL with InnoDB is RDBMS
4. InnoDB stores its tables and indexes in a table space
5. InnoDB supports transaction. You can commit and rollback with InnoDB