In an old book I have, they say that "build" is either a process of converting source code into executable or the actual result - assembly. Is that correct? Is a build actually the assembly, I mean from terminological point of view.
No, that statement isn't correct.
When you build a program the following steps happen:
Assembly is a programming language which is not machine readable until it is "assembled" (aka compiled). When assembly is compiled it becomes machine code.
Edit based on Christopher's comment: If this book is specific to .NET then yes, the terminology could be considered correct as .NET executables are referred to as assemblies.
If the book says so, then within that book, that is the meaning of the word. Obviously, in other contexts, the result of a build may not be anything usually called “assembly”, so the definition cannot apply there.
On a more general note, I don't find it odd to ask if we still have a backup of last Friday's build, so I'd say the usage of the word for the result of the build process is not entirely non-standard. English is full of words you can use as verbs or nouns, with more or less related meanings.