What is the difference between the working of C in Unix and C in Linux?

There is very little difference in the C compiler between Unix and Linux; in some cases (the gcc compiler) it is the same.

The differences come in when using system calls; some system calls do not exist in Unix or Linux, although most do. The program I work on compiles the same way (for the most part) between all commercial versions of Unix and several variants of Linux. In other words, the code is fairly portable across platforms.