The extrinsic properties of surfaces are those properties dependent on the embedding of their ambient space and otherwise intrinsic. Loosely speaking, in Weeks' The shape of space he mentioned that two surfaces have the same intrinsic topology/geometry if the Flatlander (2-dimensional creatures) can't tell them from each other while they have the same extrinsic topology/geometry if the Spacelander (3-dimensional creatures) can't tell them from each other.
For example, Gaussian curvature is an intrinsic property but normal curvature is an extrinsic property e.g. a bent square and a flat square. Homeomorphism is an intrinsic property and it's well known that trefoil and circle have the same intrinsic topology i.e. they're homeomorphic. Even more, the embedding maps are isotopic which implies isotopy type is an intrinsic property. Therefore, we have two tools to tell knots from each other: ambient isotopy and smooth isotopy. Clearly, the ambient isotopy type is an extrinsic property since it's the homotopy of embeddings of the ambient space.
Now my question comes: is smooth deformation (i.e. smooth isotopy) an extrinsic property of surfaces? I guess yes since it distinguishes knots, but I'm confused why deformation is independent of its embedding while smooth deformation does?