The transformative potential of high-quality health data in healthcare and research is widely acknowledged. Yet, the fragmented and siloed nature of health data often hinders its efficient use. Health data infrastructures - digital systems that enable the provision and utilization of health data - have emerged to address this challenge, facilitating data sharing while ensuring privacy and security. However, inconsistent terminology surrounding concepts such as health data ecosystems, platforms, and spaces complicates understanding and collaboration. This paper develops a taxonomy to systematically distinguish and characterize health data infrastructures. Including expert interviews and case analyses, we identify key organizational, technical, and data-related dimensions and characteristics. Its utility becomes evident through the classification of real-world infrastructures, revealing that infrastructures labeled with the same terminology exhibit significantly different characteristics. This taxonomy aids researchers, practitioners, and patients in navigating the evolving landscape of health data infrastructures, fostering clearer communication and improved data sharing practices.