The question requires either a book-long answer or some references. I will provide the latter. For an extensive overview of different GARCH models, see Bollerslev ["Glossary to ARCH (GARCH)"](http://public.econ.duke.edu/~boller/Papers/glossary_arch.pdf) (2009) and Ghalanos ["Introduction to the rugarch package"](https://cran.r-project.org/web/packages/rugarch/vignettes/Introduction_to_the_rugarch_package.pdf) (2022).