Ok, so a real answer for the OP.
Generally speaking, at my facility, we have 4 cleaning options. Toilet paper, disposable wash clothes which are good for mostly formed or kinda mushy/thin, but not sticky poops (these are like thin, soft and strong paper towels - they can be used dry or with soap and water, but they cannot be flushed), wash clothes and soap/water - best for sticky/peanut butter consistency or particularly foul/messy poops , and pre moistened disposable antimicrobial bath wipes (which we are not technically supposed to use for toileting, but they do get used occasionally - mainly when there is already an opened pack in the room because its better to use them than to let them go to waste). All disposable items get put in the trash, and washable linnens get put in a soiled linnen bag, which is then tied off and tossed down the laundry shoot on the floor.
My personal preference is to always use a wash cloth with soap/water for all poop that isnt perfectly formed. I feel that it cleans better and is faster. So I generally go to a room for a code brown and immediately fill a basin partially with warm water and soap (we have foaming body wash that can be used on all body parts), grab a few wash cloths and a linnen bag and then get started.
Here are your options for patients who are immobile.
Patient A - bed bound, but can turn themselves onto their side.
Patient B - bed bound and unable yo turn themselves. Very similar to this, but the second RN/CNA would roll the patient just to position the pan and then again to remove the pan. Usually, changing the sheets isnt necessary. The same goes if the patient was incontinent, you roll them like in this videa and change the soiled disposable pad under them, clean them, and roll them back.
Patient C - bariatric patient that is too large for people to roll/hold on their own for a long period of time. We position a sling under the patient (like in this video), which is then used to help roll the patient on their side. Once the patient is on their side, multiple people (deoending on the size of the patient it can be 2 to 6 people total involved) hold the patient on their side while 1 or more people clean them.
Patient D - immobile and wearing a diaper. Generally, I cut the sides of the diaper off because most adult brands do not have tabs like infant diapers (they are designed more like pull ups). Then while the patient is still on their back, i pull the front of the diaper down and fold it overhead so the soiled part is not exposed. Then tuck as mucho of that under the patients leg nearest you as you can (this makes it easier to pull out from under them). Then turn them and remove/clean/change.
Patient E - can stand for a few minutes, but isnt very stable or needs assistance. If they are wearing a diaper, I cut the sides off once they are standing, and pull it from between their legs. Once they are done on the commode, i put a new diaper on them by putting their feet in it and pulling it to their knees before they stand up. Once they are standing, i finish pulling it up. Sometimes you need 2 people to help a patient to a commode. Once to hold the patients arm and make sure they dont fall, and the other to help them wipe/replace the diaper. It just depends on how stable they are.