What is going on? The English “as” and the German “als” are related, have similar histories and play similar roles. But both modern English and modern German have decided to not let them play certain roles that they would be suited for.
As you noted, German does generally use “wie” for comparisons of alike things. In older German “als” could be used for this. Luther translates “du solt deinen nähesten lieben als dich selbst” (quoted from the entry for “als” in Grimm, I.1). And expressions as “so schnell als möglich” are deemed correct by some, even though consistency would dictate “wie” (which is consequently winning).
On the other hand, English does not like the use of “as” with the comparative. This usage is considered obsolete.
Other roles are happily shared by “as” and “als”. This is my two cents as a non-linguist (als Nichtlinguist).
Indeed, if someone would be described as “so bekannt wie Tina Turner” then that would mean that the person is very famous, if someone was described as “bekannt als Tina Turner” then we would most like be speaking of Anna Mae Bullock. (Of course, English expresses this distinction similarly, it is “as (well-)known as” versus “known as”.)