Calibration is the process of picking the parameters of the model to obtain a match between the observed distributions of independent variables of the model and some key dimensions of the data. More formally, calibration is the process of establishing the relationship between a measuring device and the units of measure. In other words, if you think about the model as a "measuring device" calibrating it means to parameterize it to deliver sensible quantitative predictions.
Estimation is the process of picking the parameters of the model to minimize a function of the errors of the predictions of the model compared to some pre-specified targets. It is the approximate determination of the parameters of the model according to some pre-specified metric of differences between the model and the data to be explained.