Both are just copper plating.
Through-hole plating is is when the masked printed circuit board is chemically treated to make the insulating insides of the drilled holes conductive. This enables the copper to deposit inside the hole, right through the board.
The hole, with plated insides, provides connection to the pads, and also to any tracks or planes in the layers inside a multi-layer PCB where the designer intended this should happen.
Straight copper plating might be used in making the large area circuit board blanks before etching.
Large-scale copper plating onto ingots weighing tons is the method of refining raw copper to high purity suitable for making electrical conductors. Also, first plating Copper onto steel, followed by Nickel, and finally micro-cracked Chromium is how we get durable Chrome finishes (eg. motorcycle exhausts). Copper plating onto metal and plastics (first made conductive) is a very common first step in plating to whatever final finish.