When modelling stocks we specify the model in terms of the dynamics of the stock itself (e.g. in Black-Scholes, Heston and SABR - often denoted $S$).
However, as I am reading about Term Structure Models many sources start with the dynamics of the short rate (often denoted $r$) or state price vector (often denoted $X$).
Why are we using this the approach as opposed to just model the bond prices directly? And what is the difference between modelling short rates and state prices?