What you feel is situational dependent, and most areas of the body to not have the acuity for there to be a difference. What I mean by this is that the majority of the body is not sensitive enough for you to tell exactly where you are feeling something, and most nerves are so small that it is well below the threshold for being able to tell where the sensation is coming from exactly. There are also different types of mechanoreceptors that perceive touch, vibration, pressure, etc. differently and occur in different amounts over the body, so there is no one size all fits answer for perception related questions. In many cases you wouldn't feel anything, it would just be numb. The pain does physically "happen" in the pain receptors which are at the end of the nerves, though our sensation and perception is not fine tuned enough for us to feel a difference.

For example, if you put two pins next to each other on someones fingers with their eyes closed they would feel that there are two pins. The fingers have high acuity because of the type of mechanoreceptor + there are many small receptors and a large amount of brain dedicated to fingers. If you put two pins next to each other on someones back, they will feel as if there is only one. The nerve anatomy is not fine tuned enough on your back to be able to tell that there are two pins, and only one receptor is activated. Now imagine you put two microscopic pins a fraction of a millimeter away from each other. You wouldn't feel two different pins because the distance is so small, which is how nerves usually are. There are bigger nerves, like the ulnar nerve aka funny bone where you can feel more localized pain though it still is not that obvious where you are feeling the pain in terms of ending vs stem.