You said nouns, so "a purchase" is something you've bought. "Do you want to see my latest purchase? It's a Ferrari". "Purchasing" could be used in the way any verb can be turned into a noun: "I like the purchasing more than the owning". Or often in companies there's a Purchasing Department (i.e. the department that buys things), and they're often referred to as simply "Purchasing". There's another meaning for purchase, which means grip. "He lost his purchase on the window ledge and fell to his death".

"Purchase" suggest that you will do something, but have not already done it (I will purchase the book). "Purchasing" is something you are currently in the process of doing. It is an action or event conceived of as having limited duration, taking place at the present time, often called the present progressive tense.