Save causes in-memory editing changes to be written back to their file(s) locally. In effect, this has nothing to do with source control — changes are changes, regardless of whether they've been written to disk yet. (However, until they're written to disk, the changes might not be visible to other SCM-related apps that you might use, such as the git command line tool.)
File -> Save saves the current file, which is the one in the currently active editing pane. You can hold down the Option key when choosing from the File menu to save all files that have changes. (The default key equivalents are Command-S and Command-Option-S.)
>> the recommended way to save changes as I go
As they say, "Save early, save often"! What you don't want is to make a series of changes, perhaps to multiple files, and lose your edits if Xcode crashes. You can always undo your changes, or use the file version browser to examine previous versions of your file(s). (Unfortunately, you can't get to the file version browser from Xcode, but you can with TextEdit — open a source file in TextEdit, and use File -> Revert to Saved -> Browse All Versions.)
>> before I want to push to Github
Most developers recommend making small commits fairly frequently, rather than waiting till you're ready to push and making one big commit. The idea with small commits is that it's easier to find a specific change, if you ever need to browse the change history in the repository. (I have a problem remembering to commit often, but in principle it's good advice.)
For those of us who have lost edit due to Xcode crashes or other similar reasons, we learn to save obsessively a few seconds after we make a change. The interval between commits is more likely to be minutes or hours. FWIW
