Random variation vs. White noise process

Correct me if i am wrong here:-When we analyse time series process we first need to convert it to a stationarity and for this purpose we extrapolate(or Remove) any trend, cycles, seasonal effects from the data so that we are only left with the random variation on top of that and then we use our modelling techniques to model this random variation.

So, my question is what is the difference between random variation and white noise process. Because, I read somewhere that it is not possible to predict white noise process(irregular movements), and aren't we here trying to model this only?