I view radicals analogous to Latin root words (e.g. aero-, anti-). So some radicals are themselves words and pictograms. However, not all pictograms are radicals.
For instance, 木 is a radical and a pictogram (looks like a tree, right?), but the words 林 and 森 all have the same root radical, 木, and are pictograms, but are not themselves radicals.
A bit of trivia, when we used paper dictionaries, words were arranged by radicals.