Basically, they're both containers, but Layers are a way of controlling selection more easily. If you have a number of layers with objects in them you can click their children without the click forcing selection of the layer. Whereas with Groups if you click you'll select the group, not the children. Also you can turn off 'Edit all layers' (bottom left button in the Layers panel) and now you'll only be able to select objects within the current layer - irrespective of whether there are things in