I had the same question. I am not a native speaker, I add quickly. When I look up the words in Norstedts Engelska Ordbok, I find "olika" more related to varieties of things (as in when all the varieties of salad dressing are on sale). As an adverb, one example is 'unequal in size', or that "människor tänker olika" (people have different ways of thinking). I was familiar with olika word from shopping (though not thinking, lol).
Annorlunda, as an adverb, can mean 'otherwise' (it says) or [helt] annorlunda [än] = [quite] differently [from]. So that makes sense with this question (to me). As an adjective, it means 'different'; the example is "de annorlunda människorna", translated as 'people that/who are different'.
This made sense to me but any expert refinements or expansions are, of course, appreciated. ;-)