Quasi-judicial power is an administrative law term, that is to say that it concerns a right that provides for the intervention of a quasi-judge, an administrative judge, who may make an order. In our system, however, quasi-judicial decisions can virtually always be appealed to the courts. So there is respect in the judicial system in place.
You can have order-making power, without being in a quasi-judicial system, which are limited to specific objects. You may grant the power to make orders without making it so the machinery as a whole operates quasi-judicially. That's an adaptation.
Then, at the other end, there is the pure ombudsman model, in which the Commissioner or the holder of the office may only make recommendations.