THERE ARE two ways to classify attractors. The first way is to ask, when are the restrictions of two diffeomorphisms to their attractors conjugate ? The second way is to ask, when are two diffeomorphisms conjugate in neighborhoods of their attractors? R. Williams has studied the first question for expanding attractors (hyperbolic structure with dimension of the attractor equal the dimension of the unstable splitting) under the assumption that the stable foliation is C’ [7,8,9]. In this note we give an example that shows these are different questions, i.e. we give two diffeomorphisms f and g with attractors At and Ae such that f: A, -+ A, is conjugate to g: A, -+ A, but there is not even a homeomorphism from a neighborhood of A, to a neighborhood of A, taking A, to AI. (They are embedded differently.) We also exhibit a technique (for this one example) that may overcome the assumption that the stable foliation is C” in the work of R. Williams. We end with an appendix that proves directly that an expanding attractor is locally homeomorphic to a Cantor set cross a u-dimensional disk. Here u is the dimension of the unstable bundle. In the example, the expanding attractor, A,, has 3-dimensional stable splitting, and A, n w’(x) is a zero dimensional set that is embedded as Antoine’s necklace, see [4] for description. The diffeomorphism is modeled on a linear expanding map, A : TZ+ T’, that is five to one. The diffeomorphism f is from T* x S’ x Dz into itself. The endomorphism A can be realized by a second diffeomorphism g: T* x D’ + T2 x D3. Then the expanding attractor for g, AR, intersects each stable manifold in a tamely embedded Cantor set, A. n W’(x). These are the two attractors mentioned above that are conjugate in the first sense but not the second. S. Newhouse has constructed a zero dimensional hyperbolic set with A fl W’(x) an Antoine’s necklace, see [5]. It is not an attractor.