Control+Z is used for suspending a process by sending it the signal SIGSTOP, which cannot be intercepted by the program.
Control+C is used to kill a process with the signal SIGINT, and can be intercepted by a program so it can clean its self up before exiting, or not exit at all.
If we suspend a process, this will show up in the shell to tell us, that it has been suspended:
+ Stopped yes
And when we kill a running process we get a shell prompt without any confirmation message.