Dan Drezner makes some mischief  with a comparison of similar statements by Hillary Clinton and Rand Paul. He offers an explanation:
The other possibility is that we’re in the very preliminary stages of the 2016 presidential election, and statements like these are sufficiently anodyne and flexible enough to allow either candidate to reference containment without feeling locked into any particular foreign policy position.
It’s true that it is still very early, and both probable candidates have little to gain from being too specific at this stage. Clinton is just as likely to make generic, ridiculous statements about “storytelling”  as she is to take specific positions, and Paul isn’t going out of his way to take positions on most contemporary issues, but I’m not buying it. Yes, Clinton and Paul are both comfortable invoking containment, but I’m fairly sure they mean very different things by them and they are using the same word to take their parties in opposite directions. After all, containment has meant very different things depending on who was defining it and how it was practiced.
Kennan famously outlined containment doctrine, but then vehemently disagreed with how and where it was applied by Truman and later presidents. When Paul refers to containment, it is Kennan’s version that he claims to have in mind, and my guess is that Clinton is thinking of containment as practiced by Truman et al. (Paul also tries to fold Reagan into his argument, but Drezner and I would both agree that it doesn’t matter what Reagan would do .) Talking up the virtues of containment in the modern GOP sends a different message and is intended to send a different message than when a Democrat mentions the concept in a long interview filled with hawkish positions . Containment was originally a dirty word in Republican circles when it first came into being, and it has become so again thanks to Bush-era support for preventive warfare. The message that Clinton seems to have been trying to convey was that she would favor a more aggressive foreign policy than the one pursued by this administration, and that seems to be confirmed by the more hawkish positions she takes in the rest of the interview. In the process, she was telling the relatively more hawkish wing of her party that she is going back to Truman and other Cold War Democrats, whose foreign policy tradition some Democratic hawks think has been neglected too much in recent years.