"I stand corrected" - you, or someone, or some information, has provided proof that I was/ am wrong, and I accept this. "I stand to be corrected" - if you, or someone, or some information, provides proof that I am wrong, then I will accept this. As GuideDogSaint says, this second iteration of the expression would often be issued as a challenge to others to prove the person wrong, or to emphasize the conviction of the speaker that he/ she is right.

The first one means someone has told you that you are wrong. You would say this immediately soneone tells you. The second one is asking for someone to tell you that you are wrong. You would say this as a 'challenge'.