Increased boldness is one of the most prevalent behavioral modifications seen in urban animals, and is thought to be a coping response to anthropogenic environmental alterations. Most previous studies have shown enhanced boldness manifested as changes in responses to humans approaching, such as reductions in flight initiation distance (FID). However, this includes two confounding factors related to “boldness”, i.e., reduction of vigilance and habituation to humans. Confounding these totally different processes could lead to our misunderstanding of urban adaptation and how to properly manage urban wildlife. Here, we propose a simple framework to separate the two processes using two flight distance measures toward different approaching threats. We considered that the distance at which targeted individuals noticed an approaching object (i.e., alert distance, AD) was related to vigilance, whereas FID represented risk assessment, which is related to habituation. We applied a predictive framework using AD and FID to Eurasian red squirrels’ responses to multiple threats of different risk levels (i.e., humans, model predators, and novel objects). AD was shorter in urban individauls compared to rural ones but not different among the approaching objects. FID was shorter in urban individauls and also varied among the objects with the shortest FID toward humans, whereas rural individuals showed similar FID to the different objects. These results suggest that while urban individuals showed reduced vigilance they could still assess different risk levels. Our framework can easily be applied to many animals and could significantly improve our understanding of wild animals’ adaptations to urban environments.