What is the difference between a Linux shell command and a system call?

A https://en.wikipedia.org/wiki/System_call is a function you use within programming languages like C, C++, Python, etc. to access functionality that the system provides through various APIs. For example, http://linux.die.net/man/2/stat is a system call - part of the POSIX standard - but http://linux.die.net/man/3/printf is not a system call - it is part of the C standard library. A shell command has nothing to do with Linux, but is a command that is implemented within the shell by the various shells in use (bash, ksh, csh). For example, bash implements echo, test, cd, but not ls. So echo, test, cd, etc. are shell commands, but ls and http://linux.die.net/man/1/stat are not shell commands. See http://linux.die.net/man/1/bash (the section called Shell Builtin Commands).

shell commands are nothing but compiled programs available mostly in /lib/bin directory.You too can write any program,compile it and then either put it in some directory already in PATH env variable or just add the directory containing your program executables in PATH env variable. system calls are operating system functions handled by os/kernel.These calls are used to access functionalities provided by os. The system calls are costly so there are lots of API available which does same task efficiently.

There is one more difference when you execute a shell command it forks a child process and entire operation is done in a separate process (different address space). On the other side, if you invoke a system call it is executed in the address space of the calling process. Performance wise using system call is more efficient.