Apologies for my answer in English, but some type of explanations still exceed my skills in German.
Der Schein makes reference to how something looks, while der Anschein, although also makes reference to how something looks, it highlights in a special way the fact that this something appears to me as such. That is, der Schein expresses a fact, whereas der Anschein highlights the aspect of movement whereby that fact comes to be.
In Spanisch, for instance, der Anschein can also be translated as
el asomo which in English is something like the emergence. Der Schein, on the other hand, is just the apperance of something.
Maybe consulting some philosophical books could help you understanding this difference in a much better way. Heidegger, for instance, explains this difference quite well in Sein und Zeit. He says that the appearance of something - der Schein - hides the fact that for something to appear as something else, that is, in order for the apperance to be, such appearance must first come to be. In this regard, every appearance entails an appearing. The former is der Schein, while the latter is der Anschein, although in regular language they are used as being the same.