Bohmian mechanics

In plain terms

Here is the problem Bohm solved in 1952: prove, by construction, that a deterministic account of quantum mechanics is possible -- something the folklore of the time, leaning on von Neumann's flawed impossibility proof, said could not be done.

The construction: particles have definite positions at all times, and a wave -- evolving by the ordinary Schrodinger equation -- guides them. All quantum predictions come out exactly. The price is explicit non-locality: each particle's guidance depends instantaneously on where all the others are, across any distance. Bell, who admired the theory, showed that price is not Bohm's clumsiness but everyone's obligation.

It remains the standing counterexample to every claim that quantum mechanics rules out determinism. Whatever else is true, that claim is dead.

In CSD

This is CSD's closest relative, and the family resemblance is real: determinism, a definite underlying state, non-locality accepted with open eyes, probabilities from ignorance. A reader placing CSD on the map should put it nearest here.

The differences are ontological and, on one point, sharp. Bohm has a dual ontology -- a physical guiding wave plus particle positions. CSD has one object, the constraint surface, with the quantum state demoted to epistemic bookkeeping; nothing guides anything. And the probability postulates differ in kind: Bohmian statistics require the quantum equilibrium hypothesis -- an assumed initial distribution, possibly relaxed into -- while CSD's measure is forced by a symmetry theorem. Where Bohmians must defend an initial condition, CSD points at uniqueness. That is the standing objection to Bohm that this programme claims to escape.

Mathematically

No formal content in the corpus about the rival itself. The shared formal shape: both derive probabilities from a measure on an underlying state space rather than postulating the Born rule -- so both owe an account of the measure, and the accounts differ (assumed equilibrium there, forced uniqueness here).