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The Intersect, Union and Identity tools can all do this with polygon inputs. They differ slightly in the way they handle differences in boundaries and the merging of attributes, but more or less accomplish the same thing when the boundaries of both input layers are identical. Intersect is available for all license levels, Union is restricted to two input layers whey you do not have an Advanced License and Identity is only available with an Advanced license.
Spatial Join can also be used if you are more concerned with summary data based on spatial overlap rather than actually cutting up all of the polygons to follow all of the boundaries of the two input layers.