Vancouver style (also referred to as ICMJE and Uniform Requirements Style) is a citation style used heavily in the health and biomedical sciences. Vancouver style uses a number to mark in-text citations, and the reference list is in numerical order according to the order in which the reference appears in the paper. If you reuse a source later in the paper, you keep the same number (e.g., source #3 is always 3, even if you use it again after source #4).
AMA style, by the American Medical Association, is based on Vancouver style. In addition to providing information on how to cite, it is a complete style guide for writing.