So, for measuring the sizes of pots and pans:
Pots are measured by the amount of fluid they can reasonably hold; pans are measured by the diameter of the surface of the bottom of the pan. Volume for the former, diameter for the latter.
If you want to buy a pot for cooking pasta, may I suggest a pasta cooker? I love mine and I've had it for years. You can buy a stock pot and a pasta insert, or for an inexpensive option, I've got something like this:
http://www.wayfair.com/Vinaroz-4-Piece-Steamer-Pot-Pasta-...
That one is about $60 and cheap, which mine was as well (I've had it for 20 years BTW). There are more expensive ones too. I like the extra steamer basket as well and have used it many times for artichokes or lots of veggies. I've made pasta for up to about 6 people in it... it gets a bit cramped, but does turn out. Plus, if you put the insert in before filling, you can add in a couple more quarts than you might otherwise. The best thing is that if you need to make a lot of pasta, set a kettle of water on to boil while you boil your first batch of pasta. Strain pasta, dump into a warm bowl, return insert to still-boiling pot and then add any extra water you need from the kettle so you don't lose your boil and voila! ready for round two (or three, or four)... Don't forget to salt the water as well.