In Business school, we were taught the differences between all the different types of companies in our new world economy. Things have changed dramatically. First off, if you were the CEO, CFO, President, Owner, Manager, General Manager, Vice President, Secretary, Treasurer, you would sign as such.
You may ask why, and that is a great question. Let me provide an example.
In the Corporate world you are considered a ? of the company, in an LLC you are considered a ? of the company.
In a Incorporated company, you are considered a ? of the company. In a Sole Proprietorship you are considered a ? of the company.
In each case in this example, the company, involves 2 or more people, even in a legally formed Sole Proprietorship. Assigning a "Principal" to your name usually involves a legal document. For instance, you may be asked to sign a new dealer application, and it may ask for a Principal owner of the company. The Principal of the company will hold legal responsibility, will own a portion, or could own all of the company. As a sole proprietorship that may mean the only legal person in which can sign the document.
The Legal Definition of Principal,
For Legal purposes:
a. a person who employs another to act as his agent
b. the person primarily responsible for an obligation
c. A partner or owner of a business.
This is primarily the only reason you would use the word principal in the world of business. In Business terms, Principal has one meaning, you would be a part of a company with a financial interest in that company. I would not sign a document, or a letter that stated "John Doe, Principal of IBM", Rather John Doe, CEO of IBM". However if a legal document asks for the Principal owner to sign, then I would sign "John Doe". If the Document asked for a signature of a Principal of the company IBM, then I would Sign "Jane Doe, Treasurer of IBM".
In non business terms, it can mean many different things. The head of a grammar school, my Principal has a masters degree, I thought they had to hold a P.H.D.! Principal in the context of a construction site, The principal of those beams come together and holds the upper floor together nicely. Meaning, many beams attached to the same place is the top load. It all depends on the context as to the meaning.
Ref: Webster Dictionary for business
Ref: Webster's Dictionary for Law
Ref: Webster's Dictionary for General terms in American English
As a footnote, one thing I can say, and repeat, it's Context, Context, Context.....