There has been considerable interest in trait correlates of excessive or problematic use of the internet, known as internet addiction. However, the concept of internet addiction has been criticised as too broad. Specific forms of excessive internet use, for example, social media, may have different trait correlates compared to internet use in general. The present study compared levels of internet and social media addiction symptoms in relation to three traits previously linked to one or the other form of excessive behaviour: alexithymia, narcissism and social anxiety. There were 217 young adult social media- and internet-using participants aged 18–35 years recruited from two university campuses in southeast Queensland, Australia. They completed an online questionnaire battery that included a demographics questionnaire and widely used, validated measures of narcissism, alexithymia and social anxiety. Hierarchical regressions indicated that after controlling for demographic variables, internet addiction symptoms were predicted by social anxiety, narcissism and alexithymia, whereas social media addiction symptoms were predicted only by social anxiety and narcissism. Results suggest that the association of alexithymia with internet addiction symptoms does not encompass excessive use of social media, and support the contention that the concept of internet addiction may be too broad.