81A is the starting designation for 85 hp Fords for the 1938 model year, and also any parts designed new for 85 hp Fords for the 1938 model year. Standard 85 hp cars are 81A cars.
Ford made a mistake when they brought out the 1938 standard vehicles, they were too plain. The initial 1938 standard vehicles had very little stainless or chrome trim. These early cars were not selling well so Ford quickly added horizontal stainless trim on the grill and trim down the side of the car. These cars still were not selling as well as Ford wanted so Ford soon again added more chrome, the chrome windshield frame. The result is three generations of 1938 Ford standard cars with varying amounts of shiny trim. By far the most produced and most common is the version with the stainless trim and chrome windshield. Below are a picture of each of these generations of 1938 Ford standard.
This has been discussed before on the Ford Barn, and is described in the 1938 Ford Book referenced above.
This is an original, un-restored, early 38 standard without side trim and with painted windshield that showed up at the 2013 Tahoe meet
This is a 38 standard with the side trim but still with the painted windshield that showed up at the 2013 Tahoe meet
This is a 38 standard with the side trim and chrome grill, the most common amount of trim on a 38 standard.
It would help if you would post a picture of your car, or email a picture to one of us to post for you.