What is the difference between "navigation database" and "airport mapping database"? Are those both required by flight management software for flight planning?
Navigation databases are typically targeted at FMS based systems, usually using the ARINC-424 standard. These are ASCII database files that describe aspects such as approach procedures, flight plans, spacing, etc. It would also provide basic runway information such as heading and altitude of touchdown points - enough to navigate but not enough to paint a completely pretty picture.
By contrast Airport Mapping Databases provide a detailed layout of the entire airport in question - runways, taxiways, vertical structures such as buildings, etc. The industry standard is ARINC-816 for the databases themselves, but the content is based on DO-272's parameters. They are usually installed into systems with displays, e.g. Electronic Flight Bags (EFBs) - this may include Class 2 EFBs that are simply iPads for ground-only operation.
Moving maps of this type provide situational awareness, especially when coupled with Cockpit Display of Traffic Information (CDTI) and its associated applications utilizing ADS-B/TIS-B: these provide awareness as to other aircraft that might be in the vicinity, threat level, etc.
Side note: additional CDTI applications that utilize ADS-B are enumerated in DO-317. These include airborne procedures, e.g. decreased spacing for in-trail procedures (ITP).