The Square (in this photo) is the new section of the Cape Quarter, and the Piazza is the older section. If you're confused by which is which, take a look at this map that I found on their website.
Something that you may not be aware of is that if you make use of the underground parking, keep in mind that the two sections (The Square and The Piazza) share one large underground parking garage. You may enter the Piazza's parking garage and unintentionally end up in The Square.