What's the difference between manufacturer's certification, certificates and statements?

From an NTEA member

We are a truck equipment distributor and recently have received more customer requests for copies of certification labels for titling vehicles in their respective states. Isn’t this the purpose of the manufacturer’s certificate of origin? 
This confusion is common and understandable. While a manufacturer’s certification label, and documents such as manufacturer’s certificate of origin, seem to refer to the same thing, they are unrelated. Compounding this confusion, several terms are often used interchangeably in the process. As such, it’s important to properly frame these two sets of requirements.

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