Pain and its management comprise an entire subspecialty of medicine, and is a very complex problem from which a great many individuals suffer. It would be difficult to even summarize appropriately all the many facts we now know about the bodily production of pain, how it is perceived, and how it is treated. To answer the definition questions, pain perception is that ability of our nervous system, to detect pain, and hopefully act to remove its cause. This is due to the pain perception ability of the nerves in our foot communicating to the spinal cord, and in turn to our brain, to notify it of a problem. The brain in turn, sends a command for action- to do something to remove the problem causing the pain.
Pain threshold is that level or intensity of pain required for our nerves to be able to detect it.
You may not be aware that a mosquito is biting you, for example, until the pain reaches your pain threshold. Pain tolerance is as the term describes, our ability to endure pain. This tolerance increases for example, with chronic pain. There are many modalities, or ways that pain is managed. In the acute setting, the health care provider will often provide medication to ease pain until whatever problem caused the pain is corrected, such as a fracture, kidney stone, or gallbladder stone.