I fear differential pressure and partial pressure are concepts that may be beyond scepti, but I'll explain them as best I can anyway.
Differential pressure: the difference in pressure between the inside of a pressurised vessel and the outside. For your average commercial airliner, traveling at 35,000ft, Shmeggly has already provided the numbers: 11.3psi inside, 3.5psi outside, for a differential of 7.8psi. The planes I used to work on went to a differential of 7psi, but they weren't built to fly as high, so didn't need the extra 0.8. Space-going vehicles operate at an atmosphere of 3-5psi, and space is approximately 0psi, for a differential of 3-5psi, less than commercial airliners, and not at all hard to achieve.
Partial pressure: you may be wondering how crews could survive with an air pressure as low as 3psi in something like the shuttle or Apollo modules? Our atmosphere is at 14.7psi at sea level, and consists of almost 21% oxygen, 78% nitrogen, and the remainder is various other gasses. The partial pressure of oxygen at sea level is 21% of 14.7, or about 3.1psi. Since all we need is the oxygen, we can therefore survive in an atmosphere of 100% oxygen at 3psi, which I believe is what they used in the Apollo modules.
Hopefully those were clear enough!