Underexpanded jets at a single pressure ratio and Reynolds number are studied in their free and impinging conditions. The influence of different kinds of aeroacoustic self-forcing is studied through Proper Orthogonal Decomposition and Dynamic Mode Decomposition analysis of high resolution Particle Image Velocimetry data. The free jet is primarily characterized by the presence of a strong helical instability, though a weaker axisymmetric instability is also present. The impinging jet shear layer is dominated by a fast-growing axisymmetric instability, with a weaker helical instability also evident. Ultra-high-speed schlieren imaging reveals a much more rapid instability growth close to the nozzle for the impinging jet case. Analysis of the streamwise growth rates via DMD suggests that the shear layer instability grows more than twice as fast in the near-nozzle region for the impinging jet. Further downstream the growth rate in the free jet case is higher.