When you play multiple units with one card, do they count as two separate times you play a unit or one?

Two — each unit is played individually, so playing two units off one card is two separate "play a unit" events, even though the card itself is only one card played.

When an effect tells you to play units, each one goes through the full Play process on its own (Rule 419.3.b — treat all steps of Play as normal). So "when you play a unit" triggers fire once per unit: Vanguard Captain's two Recruit tokens each count as a unit played (they're played, not just created — Rules 350.2, 182.1.a), triggering such effects twice.

Two caveats: the card still counts as only one card played (so Legion/"second card" style checks see one card, not two), and a trigger worded "the first time you play a unit each turn" still fires only once even if both units are played simultaneously, since the controller picks one instance (Rule 383.1.b).