mace (n.1)

"heavy one-handed metal weapon, often with a spiked head, for striking," c. 1300, from Old French mace "a club, scepter" (Modern French massue), from Vulgar Latin *mattea (source also of Italian mazza, Spanish maza "mace"), from Latin mateola (in Late Latin also matteola) "a kind of mallet." The Latin word perhaps is cognate with Sanskrit matyam "harrow, club, roller," Old Church Slavonic motyka, Russian motyga "hoe," Old High German medela "plow" [de Vaan, Klein].

As a ceremonial symbol of authority or office, a scepter or staff having somewhat the form of a mace of war, it is attested from mid-14c. Related: Mace-bearer.

mace (n.2)

"spice made from dry outer husk of nutmeg," late 14c., from Old French macis (in English taken as a plural and stripped of its -s), a word of uncertain origin, sometimes said to be a scribal error for Latin macir, the name of a red spicy bark from India, but OED finds this etymology unlikely.

Mace (n.3)

chemical spray originally used in riot control, 1966, technically Chemical Mace, a proprietary name (General Ordnance Equipment Corp, Pittsburgh, Pa.), probably so called for its use as a weapon, in reference to mace (n.1). The verb, "to spray with Mace,"  is attested by 1968. Related: Maced; macing.

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Definitions of mace from WordNet
mace (n.)
an official who carries a mace of office;
Synonyms: macebearer / macer
mace (n.)
spice made from the dried fleshy covering of the nutmeg seed;
mace (n.)
a ceremonial staff carried as a symbol of office or authority;
Mace (n.)
Synonyms: Chemical Mace