Vigilantism goes by many names:

Jeddart justice.

Rough justice.

Mob rule.

Lynching (after Judge Charles Lynch, and his activities during the American revolutionary war)

The folks who carry out vigilantism likewise have gone under many monikers:

Vigilance committees.

Committees of public safety (a name adopted at least by some groups in civil-war era Texas — and perhaps elsewhere, likely echoing “the” Committee of Public Safety of French Revolution fame).

Lynch mob.

The above terms are not, of course, all equivalent — there are important differences between, say, a Vigilance Committee set up to defend the lives and property of frontier communities, and a lynch mob pulling convicted thieves out of a jailhouse in order to hang them.