I would like to know whether I am right when I use "as" meaning: similar, equal or equivalent, and the comparative, "than", to point out a difference between the nouns.
Yes that is correct and is described in formal detail in the book:
On page 88 it describes the usage of as:
On page 87 it says:
On page 83 it says: We use comparatives to compare one person, thing, action or group with another person, thing, etc...
As a homework question, how is a comparative different than a superlative :)?
Also, you might benefit from doing the following quiz, specifically on this issue:
In fact, in your spare time, the whole site has excellent quizzes in general: