This is mostly correct, although it is a matter of dosage. People can exhibit symptoms that to the average person seem the same either because of a deficiency or an excess of the pathways amphetamine (the active ingredient of Adderral) controls.

In the case of someone recreationally taking stimulants, whether Adderall or methamphetamine/speed, they’re putting the control centers of the brain in overdrive which makes them feel pumped up and exhibit excited off-the-wall behavior.

In the case of someone with ADHD they have a deficiency that ameasured amount of the drug will address, bringing them back up to “normal” levels. Without the drug this might seem excited it off the wall with distraction, but this is due to a lack of self-control rather than too much stimulation. Even though the symptoms are nearly identical externally.

Hence the “paradoxical” effect on ADHD patients where the application of stimulants results in focused, normalizing behavior.