Technically, they were 4 bytes. Convention was to use bytes that happened to be 4 characters. Also, “that identified both” could be written clearer. There were 32 bits to identify the type and 32 to identify the creator. The Finder used the creator to determine the application to launch; file open dialogs used the type to filter files.

“When ran for the first time, programs would tell the OS what its creator code was and which file types it supported.”

It was better: when the use copied an application to a disk or moved it around, the Finder read the information from the application’s resource fork and updated the database.

“The OS would then save this information on the boot disk.”

Not (necessarily) on the boot disk; on the disk containing the application.