According Mary Kallewaard of Cokala, the program that runs TIN Matching builds a “name control” of four alphanumeric characters. For an individual, it's the first four characters of what the program perceives to be the last name of the individual. For example, that would be “MITC” taken from the last name Donald R. Mitchell.
For a corporation, it's the first 4 “significant” characters of the name of the corporation. In this example, that would be “MITC” taken from the name Mitchell Transport, Inc.
IRS Publication 1586 has a thorough explanation of Name Controls starting on page 17.
So you can see why you got a “match” for both names – the IRS methodology pulls MITC from each.
That said, you should verify with whom you have a contract. If your contract or purchase order is between you and the corporation (in this example, Mitchell Transport, Inc.) rather than between you and the individual (Donald R. Mitchell), you should have a W-9 with the name of the corporation on line 1. The corporation would be an exempt payee for which no Form 1099 is reported, unless its business is legal services or medical/healthcare services.