I bet it's different from place to place, but this is how I've heard those words used in San Diego.
When I've heard the word "kief", I've heard it to refer to what's basically loose trichomes. For example, if you have a grinder with screen, or use a screen or bubble bag 9n fresh bud or trim, the stuff that falls through is the trichomes (glitter on the bud). I heard of all those trichomes, which have sort of a powder-like consistency, referred to as kief. It's basically a pile of raw trichomes.
As far as "hash", I've heard that to refer to the result of pressing or applying pressure/heat/processing until kief/trichomes sort of becomes a different substance. For some reason it has slightly different effects if you smoke it when it's been processed as opposed to "raw". Some people roll kief between their fingers. "Scissor hash" is the trichomes and gooey stuff that collects on your scissors when you trim buds. It gets sort of dark and if you smoke it you get a different feeling than bud. You can also collect hash through a screen or making dry ice hash, then pressing the resulting kief into hash. It needs heat or pressure.
There's lots of ways to make hash, and it seems to be sort of an umbrella term for when the "good stuff" in cannabis has been processed in some way so it's no longer a loose powder like kief.
Anyways, I'm definitely not an authority, and I imagine it's different depending on where you live and but that's how I've heard those terms used
