Sometimes we have options to download the binaries of a particular software (instead of setup or source code for example).
What are binaries of a setup?
"sources" means that you get the source code, which is usually a bunch o text files (like .c, .cpp, .h in case of C/C++). You must feed these to a compiler.
Compiling then generates a binary, which is usually an .exe or a .dll file.
So by downloading the binaries you are relieved of the task of having to compile the code by yourself.
A setup will usually also contain binaries but additionally installs these properly.
A zip file containing binaries does not install anything on your system but is usually suitable for using software on a usb-drive (often called "portable" version).
Let's have a look at 7-Zip's download page:
You can download several variants of .exe, .msi and .zip files. These are the binary files intended for end-users.
The other files (.7z, .tar.bz2) contain the source code or files used for developing software that uses 7-Zip.
A setup program (or more properly, an installer) is just like a zip file full of binaries that can unzip itself and copy the binaries to the right places on your computer. The binaries are the programs, ready to be used. They're made from sources, using compilers.
Usually binaries refer to zip or installers that packages a product. It will not contain source code. It just contain files required to use/run the product. For example if you see Apache WebServer site, they will say download windows binaries for Apache MSI installer. They could have called it setup also :). So both setup/binaries are used interchangeably.
But in my opinion, binaries should refer to set of files required to run/use a product without a proper installer and setup is used to refer the case where files are properly packaged with an installer
Usually Setup files are designed to automate the copying and adding relevant registry entries, if the program has to be run during startup, adding shortcuts to the programs menu etc. Most people, like me :), don't prefer adding entries to their registry and hence go in for the binaries that are the same as the ones distributed over the setup file. All you do is just extract them to a folder you like and then execute them