Applications With Instant Approval

Earlier today, I applied for credit in two different places. One of them approved me instantly while the other did not. I know that different institutions have different standards.

It made me wonder what information is used to arrive at a decision on requests that are processed immediately. Like a computer that is the case, I suppose it has some form of. Does anyone know?

There are three major credit bureaus, TransUnion, Equifax and Experian. Most retail stores use only one or two different and may not use the same if the results may be different.
You have the right to obtain a free report on yourself once a year from everyone and you need to do to your personal knowledge to identify and protect against theft.
So every time you apply for credit drops your credit score for a few months.
Good luck.