Well "fork over" comes from the system call fork() which creates a new process. "Shell out" as explained by the author means to run an external shell command, which has been implemented in some languages by forking a shell, and then spawning the process. fork() is known as so because it results in a hierarchy where there is a parent process and a child process, and so forth. Shell just seems to be a general term for an interface used to operate an OS. [0] So no, just a coincidence.
[0] https://en.wikipedia.org/wiki/Shell_(computing)