They do it that way so it can be served quickly. The pie filling simmers away keeping warm over the serving period, and the pastry can be cooked in 10 minutes from frozen.
If done as a traditional large baked pie, the serving period is reduced as the pastry will go very dry on top, and very soggy beneath as the filling stews in a low oven. If you make individual pies and bake them fresh from chilled, it's no longer a quick meal as you'll be waiting 40+ minutes for your pie to be served, but it will be a better pie.
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I believe the way to tell the difference between the two is that a cottage has foundations i.e. a pastry base and shepherds pie doesn't. Also I believe historically that cottage pie was made from minced beef and shepherds pie from minced lamb - what else!