what you are describing sounds like what we call prn - you have to work predetermined shifts (ex. 7-3 or 7-7), but can generally pick the days you want to work ahead of time. i think this is what you were describing.
what we called per diem is something entirely different. you worked your normal 36 hours, then signed up for extra shifts above those regular hours. so, you worked your three 12-hour shifts, then could sign up in 4, 8, or 12 hour increments whenever you wanted to (but they had to be the regular increments (7-11, 11-3, 3-7, 7-3, 3-11, 7-7, 3-3, or 11-11). then, if the floor didn't need you to work those shifts, they would just cancel you for all or part of them. the upside was the per diem pay was over twice as much as regular pay, so they only used per diem nurses if they really needed them.
i really only have hospital experience, but i have never seen any unit allow nurses to work whenever they wanted in terms of shifts times. even CNAs, PCTs, techs, etc. had to work established hours unless the floor was in a severe bind.