ash (n.1) Look up ash at Dictionary.com
"powdery remains of fire," Old English æsce "ash," from Proto-Germanic *askon (cognates: Old Norse and Swedish aska, Old High German asca, German asche, Gothic azgo "ashes"), from PIE root *as- "to burn, glow" (cognates: Sanskrit asah "ashes, dust," Armenian azazem "I dry up," Greek azein "to dry up, parch," Latin ardus "parched, dry"). Spanish and Portuguese ascua "red-hot coal" are Germanic loan-words.

Symbol of grief or repentance; hence Ash Wednesday (c.1300), from custom introduced by Pope Gregory the Great of sprinkling ashes on the heads of penitents on the first day of Lent. Ashes meaning "mortal remains of a person" is late 13c., in reference to the ancient custom of cremation.
ash (n.2) Look up ash at Dictionary.com
type of tree, Old English æsc "ash tree," also "spear made of ash wood," from Proto-Germanic *askaz, *askiz (cognates: Old Norse askr, Old Saxon ask, Middle Dutch esce, German Esche), from PIE root *os- "ash tree" (cognates: Armenian haci "ash tree," Albanian ah "beech," Greek oxya "beech," Latin ornus "wild mountain ash," Russian jasen, Lithuanian uosis "ash"). Ash was the preferred wood for spear-shafts, so Old English æsc sometimes meant "spear" (as in æsc-here "company armed with spears").