volatility is a more complicated phenomenon which cannot be analyzed coherently without a proper model.
Hence, volatility is analyzed by employing a suitable model. You cannot isolate volatility analysis and volatility modelling.
GARCH like models have multi-fold applications. You can use GARCH in its original form as a measure of volatility. You can extend this model for advanced level volatility analysis by plugging in various influencing variables into the model. Then, we can call GARCH as a tool for volatilty modelling.
Your question is really more fundamental and its reflects your inquisitiveness.
Any further discussion in this regard is most welcome.
General Volatility analysis started with a basic tools such as skewness and excess kurtosis. ARCH-effect in the residuals are also indicators for volatility clustering. Once you have this phenomenon, volatility model is preferred to track and analyse the features of this fluctuations. Beside the persistence and the magnitude, you may also investigate the so-called asymmetric or news impact. In this case, many types of GARCH model have been advanced (EAGARCH, APARCH, GJR-GARCH ... )