I think those are appropriate divisions:

1. Markov process modeling - purely stochastic : appropriate for formal classical mathematical analysis
2. Compartmental modeling - could be stochastic but also could be mean-value deterministic : more empirical, c.f. epidemiology, chemistry
3. Computation realization - deterministic : appropriate for testable and verifiable systems

The first two are closely linked and are most easily distinguished by how much linearity is imposed. I have written one book that is almost exclusively on Markov models and another book that is more geared to compartmental models. The third is essentially development and engineering as you said, and my experience in this is related here: https://forum.azimuthproject.org/discussion/comment/22259/#Comment_22259