Is non-stationary the same as heteroscedastic? Are the terms non stationary and heteroscedastic one and the same? As in they both imply a variable whose mean and variance changes with time?
 A: A process whose mean changes over time but whose variance is constant is not heteroskedastic (since the variance is constant), but is nonstationary (since the mean is not).
So the answer is clearly "no".
A: There are 3 degrees of stationary. The weak form requires mean and variance are kept constant. This means that of 3 stationary definitions are stronger requirements than heteroscedasticity because heteroscedasticity means constant variance, without reference to the mean.
A process can have heteroscedasticity. But if its mean is not constant, then the process is not (weakly) stationary.
A stationary process (let's denote it by 'S') implies homoscedasticity (let's denote it by 'H'). So S --> H.
Naturally its contraposition is also true. So H' --> S', i.e. non-homoscedasticity implies non-stationary.
But the inversion and negation are not true. In other words:
"Non-stationary implies non-homoscedasticity" is not true.
"There exists a stationary process that is non-homoscedasticity" is not true.
