law firms must have their acts,  creation, or modification recorded in the competing OAB and cannot be registered in any trade board (Junta Comercial) or in the Register of Legal Entities (Cartório do Registro Civil das Pessoas Jurídicas) - more information on this type of company can be found here.

a corporation (SAs SOCIEDADE ANÔNIMA) has the capital divided into shares, and the liability of the partners or shareholders is limited to the issue price of the shares subscribed or acquired.

Corporations can be publicly traded or privately held, they are a legal entity and will always eminently be commercial in nature.

The constitution of the corporation  may be open or closed, with 'successive' or 'public' for the first, and 'simultaneous' or 'private' for the second.