First simultaneous measurements of DD and DT neutrons from deuterium plasmas using a Single Crystal Diamond Detector are presented in this paper. The measurements were performed at JET with a dedicated electronic chain that combined high count rate capabilities and high energy resolution. The deposited energy spectrum from DD neutrons was successfully reproduced by means of Monte Carlo calculations of the detector response function and simulations of neutron emission from the plasma, including background contributions. The reported results are of relevance for the development of compact neutron detectors with spectroscopy capabilities for installation in camera systems of present and future high power fusion experiments.