Difference between mod_deflate and zlib output_compression

Can anyone tell me the difference between using mod_deflate and zlib output_compression?

How can I pre-compress files with mod_deflate in Apache 2.x?

I am serving all content through apache with Content-Encoding: zip but that compresses on the fly. A good amount of my content is static files on the disk. I want to gzip the files beforehand rather than compressing them every time they are requested.