To make this precise, suppose that K is a knot in a three-manifold M (most often, M is the 3-sphere).
Context is needed to determine the usage.
When the ambient space is the three-sphere no information is lost: the Gordon–Luecke theorem states that a knot is determined by its complement.
[1] More generally complements of links are Haken manifolds.
This knot theory-related article is a stub.