Alrighty then - enough's enough.

Thanks all for your efforts, the q was harder than I thought.

To quote myself, "Any guesses as to what the common thread is?

The answer that question is "cotton".

As for the link between the two phrases, I'm told (and my sources are fallible) that both phrases arose in South East USA - cotton country.

So the story goes, when an important person sailed into the cotton ports the ship they were aboard fired one of its cannon. The bigger the bang the more important the personage. Hence "big shot".

During the Civil War there were numerous Southern society women widowed. With a need to generate an income but without a bread winner, many sought employment at the cotton mills. They were well used to turning themselves out in full corsets, but soon found these too restrictive for mill work. By loosening their corsets they were better able to do the job expected of them. The same women were obviously keen to catch themselves a wealthy mill owner and therefore were the subject of derision by their more 'common' co-workers. No doubt the notion of loose-corseted women rapidly evolved into something more lurid among the worker folk.

stales