OK,
It's Maximum Allowable Working Pressure and Maximum Allowable External Working Pressure, ( not "manufacturers...")
Apparently in the latest (2013) code changes it is now just MAWP and is stated as internal or external pressure.
• UG-116 Required Marking
Deleted the term “maximum allowable external working pressure (MAEWP)”
Clarified that “maximum allowable working pressure (MAWP)” can be either
an internal or external pressure
So in your question, MAWP is the maximum internal pressure allowed, MAEWP is the maximum external pressure allowed.
does this make sense?
Remember - More details = better answers
Also: If you get a response it's polite to respond to it.