Sounds like a different snap pea. Let the company know.

Ditto. Unfortunately, seed companies sending seed that is not true-to-type is a fairly common occurrence. On another forum, several people have complained about pea seed that is wrong, or heavily crossed.

You said "even as they are producing peas.". Have you tried the pods as snow peas? Or if the pods are a little fatter, is the pod tough or still tender?

The white flowers are a definite sign that you did not get what you ordered. Dwarf Grey Sugar can get to 4ft tall, but I have never seen them as tall as the peas you have there.

On the other hand, Oregon Sugar does reach 5ft easily, so it could be a simple mix-up. What colour are the seeds?

My OSP seeds are plain beige single coloured but my DGS are green/purple/brown and speckled.