A git repository directory normally consists of two parts. The first part is the .git directory with the real repo, that is, all files throughout history of the project. The second part is a checkout of the files (for a particular branch, like "master"), that is, the files in their current form with or without your local edits, as well as any generated or created file that is not tracked in the repo. ie your working copy.
If you zip the directory entirely, you get both parts, the receiver of the zip has whatever your current state of the project files is, and the entire history. "git clone" copies only the .git part, the history. Then the receiver can use checkout to recreate the files from the .git directory.
The thing to remember is that every git clone + git checkout is a completely self-supported independent collection of files at the file system with their history. git does store some remote access pointers, but that's merely a name translation, from "origin" to something at github.
Actual access to remote git repos is managed outside git itself. git simply uses http(s) or its own git protocol to make a network connection with the remote git instance, and once established, they can exchange revisions between the local and the remote. As part of setting up the network connection however you need access credentials, and without proper credentials you don't get a connection.
Thus unless you store your credentials inside the directory with files or inside git (ie you send sufficient credentials along with the zip), a receiver has no access to your files (he has his own files complete with history upto the time of copying the directory). If you wanted the receiver access your github repo, you would have to add him as a contributor or developer to the project, which basically tells github to give the receiver some access credentials that fits their role.
Two last things:
- For more details on this, read about "distiributed version control system"
- git is extremely flexible, I just described the common / standard setup, but you can tweak it in many ways, and depending on your tweaks some things I stated may not be true in your case.