Model estimation is the process of picking the best (according to some metric) kind and structure of model. Estimation may include calibration.
Calibration is the process of finding the coefficients that enable a model (the kind and structure of which is already determined) to most closely (according to some metric) reflect a particular known dataset.
So: estimation will set kind, structure and coefficients. Calibration will tweak coefficients, holding kind and structure constant.
Newton's model of motion is fine for most purposes. By calibrating the gravitational coefficient in it, we can make estimates of the mass of the Earth. But it won't work as a model of relativistic motion - that needs the estimation of a different model: there is no recalibration of Newton's model that works for relativistic motion - no coeffecient will work, because the model itself is simply the wrong kind and structure. It omits mechanisms and responses that are absolutely crucial, if the model is to be useful.
Similarly with economic models, Paul Krugman's point is that freshwater economists are saying that their model structures are fine, just the coefficients need tweaking. The problem with that is that if their structures are wrong, no amount of tweaking will make the models useful. Only by going back to basics, and re-estimating the whole model, would they incorporate the crucial mechanisms and responses. He argues that they won't do that, because that would require them to recognise that their existing paradigm is inadequate.