Are neural adaptation and drug tolerance to psychoactive drugs related?
Drug tolerance can be generally defined as 


  A condition that occurs when the body gets used to a medicine so that either more medicine is needed or different medicine is needed.


Tolerance to drugs can be produced by several different mechanisms. 


In the case of morphine or heroin, tolerance develops at the level of the cellular targets. Activation of opiate receptors triggers the inhibition of the enzyme adenylate cyclase. After repeated receptor activation, adenylate cyclase adapts so that the morphine can no longer cause changes in cell firing (source: NIH).


However, stating that a single target is involved is definitely an oversimplification. 

Another NIH report on ethanol dependence gives an awesome comprehensive overview of the bewildering complexity behind this phenomenon, and I will only shortly sum up the different mechanisms stated there:


Functional Tolerance develops due to brain adaptations that compensate for the alcohol. Chronic heavy drinkers show few obvious signs of intoxication even at blood alcohol concentrations (BAC's) that would otherwise be considered fatal. Examples of functional tolerance are the following:
Acute tolerance can be observed within a single drinking session. Alcohol-induced impairment is greater when measured soon after beginning alcohol consumption than when measured later in the drinking session.
Environment-dependent tolerance develops over several drinking sessions and is accelerated if alcohol administration is always in the same environment, for instance in the local pub. 
Learned tolerance develops by practicing a task while under the influence of alcohol. Rats develop tolerance faster in the context of maze walking when they have been when walking in a maze under influence for instance that practiced the task while under the influence of alcohol than rats practicing without prior alcohol administration. Likewise, people develop tolerance more rapidly if they practice a task while under influence, for instance on an eye-hand coordination task. w
Environment-independent tolerance needs larger doses. 
Metabolic tolerance results from a more rapid elimination of alcohol from the body and is caused by the upregulation of liver enzymes that metabolize alcohol. Enzyme activation increases alcohol degradation and reduces the time during which alcohol is active in the body, thereby reducing the duration of alcohol's intoxicating effects.


The metabolic tolerance is the easiest to comprehend, but the environmentally-dependent tolerance and learned tolerance, for instance, are definitely centrally mediated, but not just by one simple molecular mechanism, but by the interplay of complex neural networks governing complete and complex associations and tasks.   

Source
- National Institute on Alcohol Abuse and Alcoholism