I am new to programmming in rtem and was wondering how are the two, rtems and linux, are different in terms of programming. I understand rtems is an real time operating system but if you were to make a hello world app, wouldn’t the program be the same?
Note that your question is quite generic. There are a lot of detail differences.
One of the biggest is the format of your binary: Most RTEMS binaries are statically linked together. You only have one big binary containing your system and application. There is some dynamic loading supported but it's not the case used by most users.
As already mentioned my n.m. in the comments RTEMS has a lot of the POSIX API (at least the embedded sub set). So you can use a lot of the same API like you do on Linux.
A big differences is that RTEMS has a global address space (on most targets). So you don't have a separation between tasks. That makes pointer errors a bit harder to debug.
Also a difference: Most embedded systems are targeted for long running applications. In such applications (regardless whether you are on Linux or on RTEMS or on any other system) you should be careful to clean up your stuff (close files, free memory, ...). In Linux (or other desktop class systems) you have processes and the kernel cleans up all resources after your process exits. Although you can create threads in RTEMS no one cleans up after a thread exits.