My wife bought a brisket

Sounds like a very expensive partial brisket, but I have no clue never seen that one. Will like so see what some of the butcher experts have to say about it....

A whole brisket is usually called a "packer".  The packer is sometimes separated for retail cutting: the lean "first cut" or "flat cut" is the deep pectoral, while the fattier "second cut", "point", "fat end", or "triangular cut" is the superficial pectoral. For food service use, they are Institutional Meat Purchase Specification (IMPS)120A and 120B, respectively.