Recently, there has been a significant increase in the popularity of anonymous social media sites like Whisper and Secret. Unlike traditional social media sites like Facebook and Twitter, posts on anonymous social media sites are not associated with well defined user identities or profiles. In this study, our goals are two-fold: (i) to understand the nature (sensitivity, types) of content posted on anonymous social media sites and (ii) to investigate the differences between content posted on anonymous and non-anonymous social me- dia sites like Twitter. To this end, we gather and analyze ex- tensive content traces from Whisper (anonymous) and Twitter (non-anonymous) social media sites. We introduce the notion of anonymity sensitivity of a social media post, which captures the extent to which users think the post should be anonymous. We also propose a human annotator based methodology to measure the same for Whisper and Twitter posts. Our analysis reveals that anonymity sensitivity of most whispers (unlike tweets) is not binary. Instead, most whispers exhibit many shades or different levels of anonymity. We also find that the linguistic differences between whispers and tweets are so significant that we could train automated classifiers to distinguish between them with reasonable accuracy. Our findings shed light on human behavior in anonymous media systems that lack the notion of an identity and they have important implications for the future designs of such systems.