The quintessential example for providing source and discouraging contributions is SQLite. Nobody would argue that it's merely source available. It is full open source.

In fact "source available" usually means you can see the source code, but there are severe restrictions on the source, such as no permission to modify the source even for your own use, or no permission to create forks of the project containing the modifications, or severe restrictions on such modifications. An example is MongoDB's Server Side Public License, which is source-available but not open source.