Visa is an entry ticket

An H-1B visa is an entry ticket, issued by the state department (the U.S. consulate). An H-1B status is the lawful non-immigrant status you maintain within the U.S.
If you want to re-enter U.S., you need a ticket, either an H-1B visa or AP. The CIS guidance allows H-1B holder return to the U.S. on the H-1B visa while still maintaining AOS. However, if you only use AP to come back, you will be in a parolee status, not H-1B status anymore. You may extend H-1B to get back your H-1B status prior to the expiration of AP