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Too long for a reply, but I hope you don’t mind the answer to it:
So actually the difference is kinda straightforward ironically enough. Engraving is skill regarding engraving images into walls and floors. Stone carving is carving of stone into objects, particularly trade goods. Stone cutting is cutting stone into furniture or blocks. The easy way to tell is which station they do it at. Engravers only engrave things through the engrave command. Stone cutters are those who smooth floors, carve fortifications or minecart tracks, and work at the stone mason’s workshop. Stone carvers work at a craftsdwarfshop.
Masons btw are those that build the walls, drawbridges and other structures that need to be assembled if they’re made out of stone blocks or stones
Edit: Stone Carvers carve fortifications & mine cart tracks. Stone crafters work at a craftsdwarfshop. There’s also a recipe on the stone mason’s table that uses stone carving instead of cutting, but I don’t know which one it is. Stone cutters still smooth floors, so that information is accurate. Tbh, just cross-train your stone workers imo, excluding stone crafting. You’d rather have a strange mood on a stone cutter than a stone crafter
Dwarf Fortress is truly the game of all time.

These are all distinct skills. How in gods name am i meant to intuit the difference between Stone Carving and Stone Engraving
Come to think of it, asking a dwarf a question like that is liable to attract some strange looks. In dwarf culture you'd have to be a special kind of idiot to not know the difference between carving and engraving, after all. This is just Dwarf Fortress providing the authentic culture shock experience