BOTH. ...................

What kind of a JOB and what kind of a mistake of overcharging?

I am an employer and such an incident of an honest mistake of a small amount would not even up in your records so there is more to the story here, care to share?

As to your question there is no right or wrong depending on the rest of the story, HOW MUCH is involved?

This has to be more than not making change correctly. It probably involves not knowing your job and running up a tab on someone by selling them a bunch of stuff they didn't need. If that is it, then just proceed on and learn the job. You need to be sure you understand what the company is, the products it sells and how it sells them, in addition to the pricing and the services. It could be that this is a business/product that you don't have empathy for and you need to try a different company.

I've been a manager 

It's doubtful that any future employer would ever hear about your write ups.  About the only questions that an employer can answer are about employment dates and , "would you re-hire this person."   

The only in depth conversations are with  the people that you list as references. 

Olivia sure is a cutie pie. 

It would look worse if you went back and were fired. Because that would mean that you did it TWICE, and once after you were already given one warning. Everyone makes mistakes. I probably wouldn't hire someone that made that mistake twice.

An alligator because they can attack people and injure them