"Der Fels" and "der Stein" function pretty similarly to how "rock" and "stone" function in English. Der Fels has more of a geological or natural context and often refers to huge rock faces that you'd see on a mountain. Der Stein, one the other hand, usually describes a smaller piece of rock, often one that was shaped by human hands.
A really simple explanation that I would use with small children is that "Ein Stein ist ein Stück Fels/A stone is a piece of rock."
I've also provided you a video, because for some reason I couldn't insert images into this comment! The video has verbal explanations, definitions provided from a german dictionary, and two images to compare.