How does certegy and telecheck work?

Ok I am a little confused on this one. Certegy and telecheck are both check verifiers that merchants use. There are others but these are the two biggest ones. My question is this how do they do this and what is there criteria for verifying? I have had numerous issues with them and can never get a straight answer from the useless customer support.

To explain the problem. I wrote a check months ago for a little over 2,000. and it was through certegy. Check was approved fine. The computer never asked for a drivers license or anything. The verifier was certegy.Then almost a month later at the same store I go to write a check for 78.00 dollars and the check verifier declined it. The computer asked for my license and I gave it. The merchant had to call it in and certegy said it was declined. No explanation except a stupid useless 800 number to call. I went to another store that uses certegy and wrote a check for 92.00 and they had to call that in but it was approved?