What factors delimit terrorist attacks from other violent incidents? We develop an original news corpus of U.S. mass shooting events to examine the factors most commonly associated with terrorist-designated incidents. We first conduct a statistical analysis to identify the factors that shape whether a mass shooter's attack is designated as terrorism. Next, we verify and contextualize this by qualitatively examining media coverage of a sample of the sixteen mass shootings designated as terrorism (Global Terrorism Database). Third, we use unsupervised machine learning to discover the archetypal portrayals media ascribe to mass-shooter perpetrators. This multi-method analysis - still in its early phases - provides preliminary evidence that perpetrators with certain racialized demographic characteristics (based on their race, religion, or immigrant status) are more likely than white offenders to be designated as terrorists. In addition, we find that media sources disproportionately frame white perpetrators sympathetically while ascribing racialized perpetrators more nefarious, villainous characteristics. We close with policy and social implications of these findings for marginalized communities and discuss avenues for future research.