Hut

The only difference between a hut and a shed is what you use it for. So, when Asu unexpectedly became very wealthy and built a glittering palace next to his old hut but kept his former dwelling, partly as a reminder of his former poverty and partly as a place to store the garden implements that he now needed to look after his new garden, it became a shed.

And when Harold Evans realised that he was spending so much time in his shed that it didn't seem worth braving the cold to go back to his cold wife at night, his shed became a hut.