Direct answer: Pine tar is the general material made from pine wood. Stockholm tar is a historically important trade name for a good grade of Scandinavian pine tar.
The confusion exists because the terms overlap. All traditional Stockholm tar is normally a pine wood tar, but not all pine tar deserves the Stockholm name. Earlier trade concentrated Swedish tar in particular ports, and Stockholm became a recognisable mark in export markets.
For ordinary research, pine tar is the broader keyword. For boatbuilding, historic rigging, Scandinavian finishes, and premium heritage products, Stockholm tar is the more specific term. Both can be used on wood or rope when the product is made for that purpose, but modern product instructions should always govern practical use.
Think of the difference in the same way as material versus grade. Pine tar tells you the botanical and chemical family. Stockholm tar tells you about reputation, geography, and a traditional market identity. The label does not automatically prove composition, purity, or suitability for a project.
In short: Pine tar is the wider category. Stockholm tar is usually a recognised traditional grade or trade label. Both are associated with wood and rope protection. The best choice depends on the actual product and intended use.