The Collaborative International Dictionary of English v.0.48:

Slag \Slag\ (sl[a^]g), n. [Sw. slagg, or LG. slacke, whence G.
   schlacke; originally, perhaps, the splinters struck off from
   the metal by hammering. See Slay, v. t.]
   1. The dross, or recrement, of a metal; also, vitrified
      cinders.
      [1913 Webster]

   2. The scoria of a volcano.
      [1913 Webster]

   3. (Metal.) A product of smelting, containing, mostly as
      silicates, the substances not sought to be produced as
      matte or metal, and having a lower specific gravity than
      the latter; -- called also, esp. in iron smelting,
      cinder. The slag of iron blast furnaces is essentially
      silicate of calcium, magnesium, and aluminium; that of
      lead and copper smelting furnaces contains iron.
      [Webster 1913 Suppl.]

   Slag furnace, or Slag hearth (Metal.), a furnace, or
      hearth, for extracting lead from slags or poor ore.

   Slag wool, mineral wool. See under Mineral.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Cinder \Cin"der\ (s[i^]n"d[~e]r), n. [AS. sinder slag, dross;
   akin to Icel. sindr dross, Sw. sinder, G. sinter, D. sintel;
   perh. influenced by F. cendre ashes, fr. L. cinis. Cf.
   Sinter.]
   1. Partly burned or vitrified coal, or other combustible, in
      which fire is extinct.
      [1913 Webster]

   2. A hot coal without flame; an ember. --Swift.
      [1913 Webster]

   3. A scale thrown off in forging metal.
      [1913 Webster]

   4. The slag of a furnace, or scoriaceous lava from a volcano.
      [1913 Webster]

   Cinder frame, a framework of wire in front of the tubes of
      a locomotive, to arrest the escape of cinders.

   Cinder notch (Metal.), the opening in a blast furnace,
      through which melted cinder flows out.
      [1913 Webster]

WordNet (r) 3.0 (2006):

cinder
    n 1: a fragment of incombustible matter left after a wood or
         coal or charcoal fire [syn: cinder, clinker]

Moby Thesaurus II by Grady Ward, 1.0:

47 Moby Thesaurus words for "cinder":
   alluvion, alluvium, ash, ashes, brand, burning ember, calx, carbon,
   charcoal, clinker, coal, coke, coom, deposition, deposits,
   diluvium, draff, dregs, dross, ember, feces, firebrand, froth,
   fume, grounds, lava, lees, live coal, loess, moraine, offscum,
   precipitate, precipitation, reek, scoria, scum, sediment,
   settlings, silt, sinter, slag, smoke, smudge, smut, soot,
   sublimate, sullage