Charcuterie is a french word, it represents the processing of porc (and, quite often, duck and goose) into delicacies. Sausages, patés, rillettes, saucissons, hams, terrines, andouillettes etc… It doesn’t have a connotation of being fancy or anything. The worst ham in the world is charcuterie as long as it’s a pig’s leg that has been boiled or preserved and dried.
By extension it is the name given to a shop where this is done. Boucherie (butcher) is where beef, veal, lamb and poultries are sold, Charcuterie is for the porc (nothing prevents a shop from being both boucherie and charcuterie).
The word is naturally used to represent an assortment of cold cuts since generally most of those will be porc based or you can say that all of them would be found in a charcuterie (the shop). Therefore you would find various kinds of patés in an assortment of charcuterie althought it might be debatable whether these are cold cuts or not. Also, cold roast beef, cold chicken would be considered as cold cuts but shouldn’t be called charcuterie.
So it’s not leftovers but as an “imported” word it probably often is misused or abused to give a fancy name to common things.
Ironically, in France, an assortment of cold cuts that includes charcuterie, cold roast beef and/or cold chicken is called “Assiette Anglaise” (English plate)!