I personally would describe a patrol craft as a moderately fast sea-going gun armed (only) warship, probably with some kind of helicopter carrying (or at least refueling) capacity.
Being an old timer I'd define a patrol craft as a vessel designed to patrol a river or harbor with a limited coastal mission. The above definition would have applied to nearly every ship but carriers in the old Navy.
The first destroyers I encountered were off the coast of Viet Nam forty years ago. I look at today's destroyers and they seem more like the old cruisers than destroyers in size Guns seem to be relegated to the role of maintaining tradition. I haven’t run into a Navy GMG in years.
My war was a long time ago - and we depended on Naval gunfire for a lot of our support. A destroyer could stand near our operation and deliver a massive number of five inch shells in a matter of minutes. A gun cruiser was reason for celebration. Trouble from a tree line? Call on the Navy and the trees would disappear. Tunnels and holes on a hill? Call on the Navy and the problem would ease if not disappear. We even preferred the old prop A-1 Sky Raider to the jets. It could hang around for hours. Jets came in, dropped a load and had to leave to refuel.
Am I starting to cry in my morning coffee? Maybe. Before I retired the Army went to high tech for the sake of high tech - following the lead of the Navy. I noticed the trend in the very early 80s. Some of what we bought for the sake of high tech was junk - the LACV 30 was a good example.
The functions of the designations change with time. “Destroyer” is actually short for “torpedo boat destroyer” and was a ship designed to protect battleships from nasty little torpedo boats back at the turn of the 20th century, when these things were becoming quite a threat. Then it was realised that they were better at delivering the torpedo attacks themselves than the torpedo boats were, so they took that role on for WW1. Then come WW2 they were pressed into service as sub hunters (largely because there were lots of them) and then they became general purpose escorts, and now (in the RN anyway) anti-aircraft ships.
Guns are still useful. Missiles are more accurate and destructive and have a much longer range, but guns are cheaper and much more versatile. You got to remember that the single Mk45 5” gun on US destroyers today shoots further than the old 5” guns of the Viet Nam era, will certainly be far more accurate, and can probably pump out as many shells as three or four of the older guns. Still I take your point - the worlds navies have largely given up on naval gunfire support. In the era of the guided missile its reckoned to be too dangerous for ships to loiter close to a hostile shore. Ground support is a job for the flyboys now.