Not nesessary a deep one, but definitely a peaceful one. Also it means rest/inactivity, sometimes you could interprete it even as 'buried'. Fatigue=tiredness
"Slumber" means "sleep." I can't think of context in which it would means "rest" or "inactivity" without including sleep, and it certainly doesn't mean the same as the same as "buried" (unless you are metaphorically talking about dead people "slumbering").