Icywings-
Congrats on your opportunity to obtain some very valuable experience in a Sim. It will help you to have it.
My answer, since there seems to be various questions, is to go with the "most conservative" rule, especially when it comes to the contents of your logbook. I would say do not log "SIM TIME" in the "TOTAL (Flight) TIME" column. That column is reserved for the times you get in an aircraft with the intenet to fly. If you pay for time using an aircraft, log it! Now you have a receipt which is proof.
For those times that you want to obtain a rating that allows the use of a training aid/simulator experience to count toward the training requirements or total time requirements do so! Just look at that Simulator column and pull from the experience as the specific reg for the license you are trying to obtain will allow. With PCATD/Training Aid/etc, just be sure to ask to photocopy the letter that certifies that it meets the requirements to be certified as an applicable training aid for the particular requirement you want it to satisfy.
Level D and Level C sims are alomost identical in operation and may be used exactly for what a previous poster already said just certified for different tasks. An example of how they differ, a Level D can be used for currency simulating a circling approach, while a Level C may not.
Keep the SIM TIME and TOTAL (flight) TIME seperate and you will never go wrong, and can easily use it on those apps/resumes/or 8710's when allowed. The directions on the 8710 specifically state "Flight Simulator,
Flight Training Device and PCATD time may be entered in the boxes
provided." So even they ask that you keep this experience seperate form TOTAL TIME. Like I said, use it towards whatever a specific employer will accept, but don't confuse it in your logbook.