A dedicated test bench is employed to record acoustic emission signals from dry gas seals under various operating conditions. Time-domain and frequency-domain analysis methods are utilized to process and analyze the acoustic emission signals during start/stop, stable operation, and two common fault states (end-face defects and compensation spring failure). Furthermore, feature recognition research is conducted. A method for identifying the operational states of seals (low-speed friction, gradual detachment, stable operation) based on the root mean square (RMS) was established, with transition points at speeds of 100 and 1000 RPM, respectively. Additionally, spectral analysis is conducted using Fourier transform to determine the frequency band of acoustic emission signals (240–320 kHz) generated during contact wear of dry gas seals. Investigation into two typical faults of dry gas seals reveals that the RMS value of the acoustic emission signal gradually increases with the rotational speed during the operation of dry gas seal end-face defects. This is attributed to the insufficient dynamic pressure effect on the end face, resulting in long-term wear and tear. When the dry gas seal compensates for spring failure, the RMS value of the acoustic emission signal initially increases, then decreases, and finally increases again as the speed increases. It reaches the stable operating inflection point when the end-face speed is 800 r/min.