An ambient isotopy from an embedding of a manifold M in N to another is a homotopy of self diffeomorphisms (or isomorphisms, or piecewise-linear transformations, etc.) of N, starting at the identity map, such that the "last" diffeomorphism compounded with the first embedding of M is the second embedding of M. In other words, an ambient isotopy is like an isotopy except that instead of distorting the embedding, the whole ambient space is being stretched and distorted and the embedding is just "coming along for the ride." For smooth manifolds, a map is isotopic iff it is ambiently isotopic.

isotopy | regular isotopy