Not to be too graphic, but consider that you don’t have a lot of nerve endings until the end of your rectum, and when you get to them, they are are high alert.
When you mess, you get a clear indication something is coming out, just not a lot of info on quantity and composition. When it comes comes out, it feels like it’s piling up and spreading in your diaper. Once it’s out, it feels (on average) like you sat in warm playdoh. It feels warmer than the skin it’s touching because it carries core body heat.
Once it’s out, you might have that sort of post-coital revelation that “oh, shit, I shit myself” and rush to clean, but it’s best if you plan for a mess before you make the mess. The smell is something you can become accustomed to. You can get more efficient at cleaning it up, but the best way is usually to wipe up what you can, dispose of the diaper in a sanitary and socially acceptable manner, and clean yourself on the toilet with wet wipes… or simply take a shower.