Forgive me for being a little nerdier than usual here, but this may interest you, too. In the Pali Tipitika, the Buddha talked about "mental factors" (cetasika) and "feelings" (vedana). Very basically, "feelings" refers to the sensation that happens when a sense organ bumps into a sense object. For example, an ear plus a sound creates the vedana hearing.
Some teachers also talk of emotions -- mental pleasure or pain -- as vedana. The important point is that like the sense organ finding a sense object, these emotions also have an object, some phenomenon that triggers pleasant or unpleasant emotions. If buying new shoes gives you a temporary happiness fix, that happiness is vedana.
Vedana is a type of mental factor, but there are others. Mahayana and Theravada have slightly different lists of mental factors, but vedana is prominent on both lists. Other examples of mental factors are volition, perception, mindfulness, and samadhi, as well as greed and delusion.
When the Buddha spoke of cultivating happiness, he was not talking about vedana happiness but about piti. Piti is a mental factor that is translated into English as "happiness" or even "rapture." The significant thing about piti is that it is not dependent on an object. Phenomena and situations come and go, but the person who has a mind of piti will remain unaffected.
I think it's useful to have some grasp of this, because "happiness" can be a lot of different things to different people. I tend to think of happiness as an ephemeral thing that is here today and gone tomorrow, but that is ordinary happiness, not piti.
Sometimes defining terms helps me a lot.