The X.509 public-key certificate or the X.509 attribute certificate, as defined by the ISO/ITU-T X.509 standard. Most commonly (including in this document), an X.509 certificate refers to the X.509 public-key certificate.
NIST SP 800-57 Part 1 Rev. 3 [Superseded]
NIST SP 800-57 Part 1 Rev. 4
Public key certificates that contain three nested elements: 1) the tamper-evident envelope (digitally signed by the source), 2) the basic certificate content (e.g., identifying information and public key), and 3) extensions that contain optional certificate information.
NIST SP 800-57 Part 2 under X.509 certificate