Pet wearables are increasingly prevalent, with many incorporating location-tracking functionalities, which may reveal privacy-sensitive data about their owners' daily patterns. Typically, these devices are designed for cat (felis catus) or dog (canis familiaris) usage. However, the difference between cat and dog owners in how they interact with their pets, and the relationship they have with them may lead to differences in the perceived sensitivity of, and requirements for, the way these pet wearables should handle pet location data. We present the results of an empirical between-groups study (N=180) investigating whether cat and dog owners' information privacy concerns for pet location data differ. We also explore the role played by the pet-human bond in this context. Our findings indicate that there is a significant (p<0.01) difference in bonding between cat and dog owners explained by co-sleeping and closeness factors, which leads to a significant correlation (r=0.26) found only among dog owners between the strength of their bonding and their perceived importance of how the collected pet location data is used (p<0.05). We demonstrate that the relationship to our pets, not their species per sé has an impact on the privacy concerns held towards data collected via wearables. These findings have implications for the design of privacy-respectful pet wearables, emphasizing the need to understand how sensor-driven technology's privacy impact is mediated by the way we interact with different species. We discuss what explanations may underlie these findings and to what extent, and how, manufacturers and policy should take such differences into account.