CORRECT. I can only speak for Maryland but First theres the stop for whatever traffic violation, (speed, lights, swerving etc), then theres the initial contact where the officer observes the driver and sniffs. Thats followed by field sobriety tests (one leg stand, walk and turn, etc), The if trained the officer does a Horizontal gaze nystagmus test (shaking eyes) and possibly a field breath test (preliminary breath test-not evidence), and makes a decision whether or not to arrest
IF arrested and IF the driver elects to take an actual breath test AND if the test shows 0.0 alcohol then a Drug Recognition Expert is called in to do further visual tests on the driver (pupil size and reaction time etc), and if that indicates drugs (and which type) the driver is taken for a blood draw