Amphetamines displace amine neurotransmitters from their vesicles in the neurons, causing them to build up in the cytosol. This leads to an accumulation of dopamine and noradrenaline extracellularly, but not resulting in an action potential forming.
Cocaine inhibits the uptake of amine neurotransmitters, causing them to remain in the synapse for longer. This increases motor activity, as well as leading to feelings of euphoria. The euphoric feelings lead to addiction.