There is not a true consensus on the use of the terms.
Many people use painting and coating interchangeably, and "painting" is often used to mean any thin-film liquid-applied covering. However if pressed to distinguish:
"Painting" is more often decorative as its primary function.
"Coating" is primarily protective of the substrate as its primary function.
"Lining" is internal (tanks and pipelines) and is protective of both substrate and content.
Again, these are not universally and firmly agreed-upon - usage is quite varied.
ASTM D16 is a good resource, but far from comprehensive - even in the ASTM D01 committee, different subcommittees and standards have additional definitions which have not made it all the way to D16. Plus, there is also a joint ASTM/NACE committee (J01) which has developed a 28 page set of definitions "Terms and Acronyms Relating to Corrosion" - which is still pre-publication.
My absolute favorite paint nomenclature reference is the "Coatings Encyclopedic Dictionary" put out originally by the Federation of Societies for Coating Technology (FSCT) in conjunction with ASTM - the FSCT was later eaten by the American Coatings Association (Paint.org)
Sure - a powder coat is typically just a paint (or coating. HA!) which is liquified by heat instead of solvents for application. It still fits in the liquid-applied portion of the requirement and creates a film. You might quibble that it only liquifies after hitting the substrate - I contend that in order to form the film, it liquifies, so it counts.
Thermoplastic road markings also count - similar to a powder coat in that heat is used to liquefy instead of solvent, but liquified in bulk rather than by a heated surface.
