Specialization tokens add "traits" to the squad. Most of those traits are continuous effects, like Anti-Tank's "Armor-Piercing Weaponry" trait that adds +3 firepower and increases their base range to 3 when attacking vehicles. Those traits do not require taking an action.
Some traits, however, allow the unit to take special actions. The description of those traits will all contain the explicit phrase "as an action". Examples are Medic's "Heal" and Engineer's "Dig Entrenchment". In those cases, you must expend one of your three actions in an action turn to activate that trait. (See the definition of "Special Action" on page 12 of the rulebook.) These actions generally Fatigue the unit, so you won't be able activate the unit again.
So, you cannot both Move your Medic and then Heal a unit using that Medic in the same round.