Yes, KS is "physical modelling". The term is useful to distinguish from spectral modeling. With spectral modelling you try to emulate a sound by directly following the spectrum at some points and with physical modelling the implementation tries to copy the physical process going on, to some extent, following the propagation of forces and displacements, boundary reflections and phase inversions..etc. But there isn't one way of doing PM.
KS is an example of a waveguide model, as opposed to a discrete MSD (mass-spring-damper) system. It is really a kind of IIR (recursive) filter.
I have seen two interesting string pluck implementations in Pd. The proper way, (as done by P Cook and JO Smith) uses two delays, one for each direction of propagation, and two filters which represent the end reflections.
Syntax the Nerd made a nice pluck unit using the fast t3_envelope and small blocksize in the Bot collection.
If the duration of the excitation is greater than or equal to the buffer propagation time, and a copy is passed straight through to the output, then the noisy attack leaves no perceivable delay at the start of each note. Unless the blocksize = 1 it gets hard to tune high notes.