In GIMP, the alpha channel and the mask achieve the same thing but they are two different entities.
You can see that they are stored separately in the Layers doc (the vertical vs. the horizontal stripes)
While I did not check the source to confirm this is indeed the case the behavior seems to be as follows.
An "effective alpha" is computed as:
alpha[per pixel]*mask[per pixel]*layer opacity
this is used as:
effectiveAlpha[]*layerBlendResult()+(1-effectiveAlpha)*layer(s)Below
This becomes especially interesting when you are using a different blend mode than normal.
Whey you have a look at the channels dialog though you will see the effective alpha (all visible layers) rather than the layer alpha.
(yes, it does include the layer alpha at least as of version 2.8.2)
The significant difference is in how you can edit them:
Alpha can be transformed into mask when creating a new mask.
The mask can be transformed into an alpha channel by doing mask->selection, Delete