I hope that my question will be suitable for this forum: I would like to understand the difference between the so called consistent history approach to QM and several other interpretations. In this discussion it is remarked that similarly to the many worlds interpretation, there is no wave function collapse in the consistent history approach: the collapse is only apparent and is caused by the interactions with the environment, in the so called decoherence effect. But there are big differences between CH and MWI: CH is fundamentally probabilistic while MWI is deterministic; there is one world in CH (but there are many ways of describing it) while MWI carries ontological baggage: all branches are no less real than our branch. So I would agree that these approches are quite different.
However, if insetad of MWI I switch to relational interpretation (by Carlo Rovelli) or to QBism, these differences disappear: both interpretations (relational and Qbism) are probabilistic and both assume unique world: in relational approach we speak about properties of the system with respect to another system, in QBism we speak about properties with respect to agents: in CH the role of the system/agent is, as far as I understood, played by a ,,set of questions which we would like to ask'' (the so called framework). I don't see where the difference lies beside slightly different philosophical flavour of way of putting it. So I would like to ask:
In which sense is consistent histories interpretation different from relational interpretation and from QBism?
Also, I believe that QBism became much more popular nowadays and CH interpretation seems a little bit forgotten:
Why was consistent histories interpretation abandoned by a physics community?