I am not sure if you can classify it like that. Mind you, I never wrote a book. I'll write what I know below and you can decide if the classification makes sense or not.
1 ) STIR: as the term indicates - short term like Eurodollar frequently modelled with Black or Bachelier (normal) model. HW1F is also a short rate model.
2 ) HJM is a framework (M is not ...
If we take your model literally (with the correction that I suggested as a comment), then there exists no (semi-)closed form, IMHO, that you can use for asset pricing. What you could do is then to make the model a bit simpler or to simulate.
This is the nasty part. Based on your model, you simulate a very large number of the discount factor(s) and ...
Just an addendum to the above answers and comments:
The main decision is whether to use single or multiple factor dynamics.
LMM models term forward rates. HJM models instantaneous forward rates.
The main disadvantage of HJM, high-dimensional
stochastic process as underlying, was overcome by Cheyette, back in 1994, by restricting the general HJM model to a ...