Boldness in animal personality studies is measured using a range of different behavioural assays, including responses to novel objects, novel environments and threatening stimuli. These assays should be correlated if they all reflect boldness, but this assumption has rarely been tested. We investigated experimentally whether presentation of threatening stimuli (a taxidermic puff adder, Bitis arietans arietans) and novel object (an unfamiliar food item) both assayed the same personality trait in wild chacma baboons, Papio ursinus. We recorded individual responses to both the snake model and novel foods for 57 baboons encompassing all age-sex classes in two study troops over 3 years. Surprisingly, those individuals that showed the greatest alarm responses to the model snake, that is, the least bold responses, also inspected it for longer. Furthermore, individuals' threat responses did not correlate with their response to the novel food. Thus, boldness according to one definition was not related to boldness using another definition. We suggest that threat-directed behaviours did not reflect individual boldness, but instead were indicative of another personality dimension: anxiety. These findings highlight that current boldness assays may not be interchangeable, and in some cases may not measure boldness at all. We stress the value of using multiple assays to measure the personality trait of interest.