Why does pistachio ice cream not taste like pistachio nuts?
Firstly, let me disagree and say that I have tasted some (amazing) pistachio ice creams that tasted very much like the actual nuts. That said, I can think of several reasons why the ice cream might taste differently from the nuts:


Artificial flavours, like you suggest. You might be able to figure out from the ingredients list if these are used.
Salt. If you have only eaten salted pistachio nuts, you might have a different benchmark for pistachio flavour. Salt is a flavour enhancer, after all.
Temperature. The temperature of food and drinks radically changes how it is perceived when tasting. This is why (bad) coffee is OK when hot, but terrible when at room temperature, and why melted ice cream tastes much sweeter than the frozen stuff.


A final side note, which I include mostly because I find it interesting: I used to think 'banana flavour' was based on a different type of banana than commonly found in stores. Doing some searching for this question, it turns out I was wrong.