Not a Dr here, but to offer my two scents on both questions, they're generally feeling for masses, bumps, or to determine where the discomfort is coming from, if any, which may determine more comprehensive tests or equipment.
Given their experience with these procedures and historical training, they know what the internal lining feels like, whether smooth and moist, or rough patches, polyps, pain, etc. Was there any abnormal fluid on the glove, etc. For an easy comparison, an experienced drywaller can see blemishes and warping, where I only see a wall with no obvious problems.
Your effort when feeling a healthy rectum may not yield much except the sponginess, which is the desired assessment.
Regarding the other post, you can always google that part of your anatomy to see what organs are in those areas, to include calling your Dr and asking to understand more about the procedure(s) so you're better informed, which might also help if that problem happens again and you're able to explain in better detail.
In my experience, physicians appreciate when I've done my homework and try to help as best I can when diagnosing a problem.