Biometric research is directed increasingly towards Wearable Biometric Systems (WBS) for user authentication and identification. However, prior to engaging in WBS research, how their operational dynamics and design considerations differ from those of Traditional Biometric Systems (TBS) must be understood. While the current literature is cognizant of those differences, there is no effective work that summarizes the factors where TBS and WBS differ, namely, their modality characteristics, performance, security and privacy. To bridge the gap, this paper accordingly reviews and compares the key characteristics of modalities, contrasts the metrics used to evaluate system performance, and highlights the divergence in critical vulnerabilities, attacks and defenses for TBS and WBS. It further discusses how these factors affect the design considerations for WBS, the open challenges and future directions of research in these areas. In doing so, the paper provides a big-picture overview of the important avenues of challenges and potential solutions that researchers entering the field should be aware of. Hence, this survey aims to be a starting point for researchers in comprehending the fundamental differences between TBS and WBS before understanding the core challenges associated with WBS and its design.