Methylphenidate is a dopamine/norepinephrine reuptake inhibitor.
Amphetamine is a dopamine/norepinephrine releasing agent.
Methamphetamine is a dopamine/norepinephrine/serotonin releasing agent that metabolizes into amphetamine.
What this means for the layman -
Methylphenidate is 'similar' to pharmaceutical cocaine - some people prefer it to amphetamine and get clean stimulation but many find it feels "tweaky", has a horrible 'crash' or makes them paranoid and jittery, especially in high doses.
Amphetamine is similar to a longer-lasting methylphenidate that is more "intense" in general. It generally causes a good degree of perhipheral side effects like sweating, vasoconstriction and flushing. It's also a lot more fat soluble so it has a slower "comedown" than methylphenidate. Overuse can lead to hangovers and tolerance, much faster than with methylphenidate.
Methamphetamine is like a very long lasting, "smoother", more euphoric (generally) and stronger version of amphetamine. The major difference is that the total half life for the stimulant is almost 24 hours (6-12 hours for meth->amp, 12 hours for amp->inactive). It's also considered neurotoxic whereas the other two are not.