Does NASA's use of the term launch vehicle apply only to those that ascend from the Earth's surface and leave the atmosphere? If so why is the term limited that way?
I'm going to propose this as a tentative answer.
In this context "launch vehicle" might refer to the first, original launch from the body on which the payload originated. Until now, payloads are launched from Earth† using rockets.
Some fraction of the payload and some samples might be launched again by other parts of the original payload, but that doesn't necessarily make them "launch vehicles".
The OP has provided several random NASA links as examples:
- Glenn Launch Vehicle History
- MRO Launch Vehicle
- Curiosity; What is a Launch Vehicle?
- Mars 2020; What is a Launch Vehicle?
- Insight; Launch Vehicle Summary
These pages generally explain that a launch vehicle is used to get a spacecraft off of the Earth, to do the work of escaping Earth's gravity.
But that doesn't mean necessarily that NASA would never use the term when launching from a different body.
When the Apollo astronauts launched back into space from the surface of the moon, the action can be called launching but the ascent vehicle is still just a part of the Saturn V's original payload. It wasn't built on the Moon as a launch vehicle. There were some sample return functions, but lunar module and its inhabitants originated on Earth and were launched from there.
I don't believe that spacecraft launching from the Moon or Mars will ever be considered as "launch vehicles" until at least they sit there for a while and are at least refueled and prepared for their launches in some way.
Still, because of the reduced requirements of launching from those lower mass bodies with less or no atmosphere than Earth, they may be called lunar launch vehicles or Mars launch vehicles. I'm guessing they won't be called martian launch vehicles because of the historical use of the term martian to refer to something else.
Feel free to edit, vote up or down, or comment. I am not sure this question can have a source-able answer.
†or occasionally launched slightly above Earth's surface from planes or very rarely from balloons