Suppressed means there is continued transmission, contained means that’s stopped. Rabies is suppressed with a continuing threat from wild animal populations. The recent Ebola virus outbreak on the other hand is an example of containment in action, with zero active cases at this point.
The only long term success for suppression is from a vaccine. Contained on the other hand means every infected person can gain immunity and the virus would then run out of new hosts.
Yeah, if they stop containing it, it will start spreading again...