It depends
If the web store is a separate business, then yes two separate company files, separate inventory, etc etc, and yes you file a schedule C for each
if the web store is an extension of the present store, will sell inventory from it, etc - then no it is the same company, so the same company file.
A web store reports on sale, tracks customers, etc etc there is no reason to duplicate that data in QB, just enter a summary sales transaction daily or weekly or ...