The arresting officer is the officer who made the arrest, the one who actually puts the handcuffs on the person. The arresting officer is not necessarily the reporting officer, who wrote the police report, or the investigating officer, who is the detective. They may be the same person, or they may be different people. In a typical sting or buy/bust, the arresting officer is usually a uniformed officer who waits for a signal by the undercover officer, who then comes in and makes the arrest. Handcuffs tend to be noticeable if you're wearing street clothes.

Booking is the process at the jail where the arrestee is fingerprinted, processed, and classified for a more permanent location. That can be handled by city police officers, county sheriff deputies, or even civilians, depending on the place.

I'm curious as to why you want to know the identity of the arresting officer. Are you trying to contact him or her?

The arresting officer is the officer who arrested her. Not necessarily the guy who made the appointment. I'm assuming this was a sting and most stings are run by more than one cop. The arresting officer may have been the same guy that made the appointment but it could also be another cop who was on the scene. If she was busted in a sting she was already under arrest before she got to the station.    The arresting officer would not be someone at the station.

The arresting officer is usually the one who identifies himself to the provider as LE and tells her that she is under arrest.  For stat purposes, it is the officer who writes the report and, as such, includes the names of all of the LE officials who were involved in the sting...the providers are very wary of these situations so the LE who makes the phone call is usually the LE that shows up for the appointment just from a voice recognition and conversation style standpoint.  Note that these stings are usually done in hotels for outcalls because LE has more control over the sitution and minimizes the unknown factors which then minimizes the danger to LE

Often, the involved eyewitness cop is part of a local regional task force.  He or she often is affiliated with a nearby jurisdiction so that locals will not recognize him or her.