I've seen NLU and NLG described as areas within NLP.

I think generating headlines from an article would use a bit of both. A pure NLG task would be more like creating sentences to describe the weather based on weather data, or medical data on a patient, etc.

I'm not an expert in the field though, really just a beginner so my understanding may be off.

That acronym isn't broadly known, so less useful. Also, NLP seems like the encompassing term (The "P" for processing can mean reading/parsing, translation, and also generating).

Yes it is. NLG is the sister field to NLP.