Does each format need a different ISBN?

Yes. An ISBN identifies a specific format, so each edition of your book gets its own:

• Paperback → one ISBN
• Hardcover → a different ISBN
• Ebook → another (or Amazon's ASIN, if you don't assign one)

An audiobook would take yet another. The copyright page conventionally lists each on its own line ("Paperback ISBN: …", "Hardcover ISBN: …", "Ebook ISBN: …"), and the Front Matter generator provides a field for each format you're publishing. If you're using free KDP ISBNs, KDP issues a separate one per format automatically.