AirMap is far superior to B4UFLY, in my opinion.
There's no legal requirement to use B4UFLY.
If you are flying a Part 101 (hobby/recreation) flight, you still need to contact all airports if you are flying within 5 miles. And for Class B airspace, you must receive authorization from the tower before you fly. For other airspace, you are only required to notify the tower.
If you are flying a Part 107 flight, then you do not need to contact airports that do not have controlled airspace (ie are Class E and Class G).
For Class B, C, and D airspace, you need a waiver or authorization from the FAA before you fly in that controlled airspace.
You can notify some airports through the AirMap app using the LAANC program which is slowly being rolled out. You have to initiate this notification in the app. It's not automatic.
It’s Official: Nationwide Expansion of LAANC to 500 More Airports Begins Next Month - AirMap
FAA UAS Data Exchange
Otherwise, you have to apply through the FAA website and wait for the authorization to be approved.
Request a Part 107 Waiver or Operation in Controlled Airspace