HERE is a pretty comprehensive site for license plates.
From what I'm seeing for Illinois, they had a few years where plates were carried over with new date stickers, instead of issuing new plates each year. I'm sure many states also used the multi-year plates with either bolt-on tags or other methods for subsequent years. I know that California did that quite a while back, as early as 1916. Wisconsin also did the same in 1943 with tabs.
LINK 
