There are a few differences on Linux.
First, I don’t believe there is always a single keystroke available to copy something to the clipboard. Control-C may work but you may need to test (locally on the SUT) with that specific application and see what works.
Second, it could be because of the way the clipboard was implemented in the application you are testing. There are two mechanisms for implementing *nix clipboards, and only one of them is visible to VNC. The latest release of RealVNC for *nix includes an application called vncconfig. Here are some relevant notes from the documentation:
When run with no options, it runs as a kind of “helper” application for Xvnc. Its main purpose when run in this mode is to support clipboard transfer to and from the VNC viewer(s).