In the setting with nonnegative Ricci curvature and a uniform lower bound on volume, the GH and SWIF limits agree.
[1] Wenger's compactness theorem states that if a sequence of compact Riemannian manifolds, Mj, has a uniform upper bound on diameter, volume and boundary volume, then a subsequence converges SWIF-ly to an integral current space.
[1] An m dimensional integral current space (X,d,T) is a metric space (X,d) with an m-dimensional integral current structure T. More precisely, using notions of Ambrosio–Kirchheim, T is an m-dimensional integral current on the metric completion of X, and X is the set of positive density of the mass measure of T. As a consequence of deep theorems of Ambrosio–Kirchheim, X is then a countably Hm rectifiable metric space, so it is covered Hm almost everywhere by the images of bi-Lipschitz charts from compact subsets of Rm, it is endowed with an integer valued weight function and it has an orientation.
A 0-dimensional integral current space is a finite collection of points with integer valued weights.
[1] All the above mentioned results may be stated in this more general setting as well, including Wenger's Compactness Theorem.