Quote Originally Posted by it-ogo View Post
It is called subjunctive rather than conditional. The difference is that subjunctive implies that the mentioned condition is not really fulfilled, that is purely imaginary.

"б" and "бы" are two forms of the same word.
The term subjunctive is mostly used in Russian textbooks of English. Most English language grammar books call it second or third conditional (the second conditional is past+would, the third is past perfect+would have), or unreal conditional. In any case, you're correct that it refers to an imaginary condition.