Is the kind of methamphetamine doctors sometime prescribe, the same stuff people cook up illegally?

Typically yes.: There are several methods to produce "meth" -- some of these are similar if not the same as medicinal α-methylphenethylamine.

Related but not same: The meds like Adderall (dextroamphetamine and racemic amphetamine) are a complex blend of several amphetamine salts that are produced with a reliable purity and strength.While similar in basic structure to "cooked" material, the production controls and blending process is where the similarity ends.

Sort of: Physicians typically are using a slower release longer acting amphetamine as opposed to the illegal drug, which is short acting for the intense high and effects.