Spectrum analyzer is often the analysis of the frequency composition of the input signal. The signal analyzer is used to analyze the characteristics of the signal.
From the visual display, a spectrum analyzer is shown for each frequency point on line which frequency signal is stronger the higher the bright line.
The signal analyzer shows the full waveform of the signal. You can analyze the frequency of the signal, the cycle, the magnitude of the distortion and so on by means of an instrument.
Of course, newer analyzers are versatile, called synthetic testers. It can almost do most of the work of measurement.