19v Charger with 14.4v Battery: What exactly can I expect?
The wall adapter probably doesn't connect directly to the battery.  There will be a battery charger circuit inside the laptop that decides whether and how to charge the battery.  Most likely it's (partly) a switching regulator that needs an input higher than its output and thus the wall adapter voltage will always be higher than the highest voltage the battery can reach while charging.  You shouldn't expect the voltage spec on the adapter and battery to be the same.

The battery charger circuit inside the laptop will need the correct input to function properly, but it's possible the manufacturer designed the laptop to accept more than one of its own wall adapter models.  The battery may charge faster with a higher-powered model (more current capability) and slower with a lower-powered one.  One would hope the vendor designed its own laptops to accept input from all of its own wall adapters with a plug that fits (otherwise they'd have put a different plug on the adapter to avoid confusion, circuit damage, lawsuits etc.).  It would be best to ask the manufacturer directly.