Why are demiliches higher level than liches?

The entry on AoN basically describes demiliches as degraded liches; their soul cage is lost, their body disintegrates, their soul leaves the mortal dimensions, and all that's left is the skull and magical power and artifacts they left behind. To me, that sounds like a degradation; the vestiges of power leftover from them basically dying. Even the prefix demi- implies this, meaning half. Half a lich, so I'd assume less powerful, and in the case of runecarved liches this holds true, but horde liches are the same level as a demilich, and the regular liches are even lower level! I don't see how this makes any sense; the leftovers of a lich shouldn't be more powerful than the lich once was. Are demiliches only formed from the remnants of a runecarved lich? What's going on here?