Ooh. I've got this one. You see -- you've answered your own question:

"Love" refers to a bond between two people (e.g. romantic) or among many people (e.g. familial, tribal). It's an emotion which, along with others, compels social harmony. It's what encourages us to work together, and this is what benefits our survival.

"Grief" is the flipside of that. It's the consequence of the bond being severed. Which I suppose could further compel you to protect that bond, to fight for the survival of not only yourself, but also of your mate and your tribe. But mostly it's the consequence to losing a loved one. When a bond is severed, it's a bit jarring (in theory). It takes some time to process and recover, and that's where the "grieving process" comes in.