No, XP is not short for "[life] experience." It just means "eXPerience", period. D&D introduced it four decades ago. In RPGs, it stands for ANY experience the character has that is deemed to be worthy of increasing abilities in some way by the DM/GM.

And yes, this means that a trip to a store to buy milk might very well result in XP gain. It all depends on the decision/judgment of the DM/GM, not on any predefined criteria.

Combat is absolutely NOT important for XP gain. Encounters in general are not important, for that matter.

Any activity, any at all, may result in XP gain. It all depends on context.

By the general rules of Game Mastering, Tenshi is right.