So long if you're able to recover versions of your work, it is version control. I am sure before the geeks came up with those fancy high tech systems, people were already doing this in business and government for recording their business activities.
If you're talking about source codes, there are better things like Git and svn that you have mentioned. And Github is not the only service on town.
Hosted service: Look for private repository if your project is private and proprietary. Places like BitBucket or GitLab may provide private repository.
On-premise hosting: An alternative is to have you own machine on your own private LAN to host the repository. But you need to setup the system and version control software of your choice.
For distributed version control systems, you don't even need to check in to a server. Your can check in locally to your local repository on the same desktop/laptop/workstation, which is usually a special local directory or folder on your HDD. Just don't mess around with or poke the files inside which may corrupt the repository.