Ah. Great question. There are many correct answers - it's like asking "how should I make a sandwich?". Let me count the ways...
If it's the same business entity controlling inventory for both POS, then use a single database for sure. Knowing the number of items in stock for both POS is nice.
Are both sites hosted on the same server? Then use one database, because it's easy to connect both of them to the same DB.
If the business logic for each site is different, then consider building a DAL (Data Access Layer) to interact with the DB, with custom methods for the interface, with stored procedures hidden beneath.
If, someday, there will be 3, 4, more sites all using the same data, or if the sites will be hosted on disparate servers, then building your DAL into a REST service is useful. (make sure it's secure!)
Will you need to export this data to the public? If so, then an XML feed is a good idea.