The difference between merken and bemerken is at the formal level, in shades of meaning and in other meanings of these words. Additionally, let’s take the words wahrnehmen, erkennen, sich erinnern, einprägen, memorieren.
As you can easily guess, the root of the word comes from Marke – a mark. Hence all the meanings: made a mark – remembered, made a mark – noticed, made a mark (verbal) – that is, made a remark.