Warlord is a unit that has Leadership abilityErf-b1-p040aErf-b1-p084a. That special (or natural) ability allows Warlords to lead other units in combat and grant a bonus to units under their command.
On some occasions terms Warlord and Commander are used interchangeably.Erf-b1-p040a
However, Commander is a more general term since Casters are Commanders tooErf-b1-p084a, but they do not have Leadership ability.
Infantry units can be promoted to warlord in the capital (although at a high cost)Erf-b1-p043a or popped.
Chief Warlord is not a separate class, but is a subclass of Warlord. A Chief Warlord provides bonuses that other Warlords do not.
Ruler seems to be a separate class of Unit (Rulers grant units in their stack a bonusErf-b1-p115, but it is not clear whether that bonus comes from Leadership ability or as a result of some special rule).