360K Floppy in 1.2M Drive
Writing to (which includes formatting) a 360K floppy in a 1.2M drive results in a 360K floppy that does not conform to the 360K standard.
If that floppy is then placed in a 360K drive, the drive may or may not be able to read the floppy.
In the IBM DOS 3.3 reference, IBM includes on the subject, "IMPORTANT: If you write on any of these diskette types using a high-capacity drive, you may not be able to read the diskettes in a single-sided or double-sided drive."
Technical information on the subject is at here.
This problem is why IBM offered a 360K drive as an optional extra for the IBM AT (IBM 5170). IBM AT customers who needed to create/write 360K floppies for others that only had a 360K drive, would use their 360K drive rather than the 1.2M one. As a result, 'true' 360K floppies were created, and the recipient's 360K drive guaranteed of being able to read the floppies.