If the existing terminology doesn't quite fit the application you are interested in try to build your own, then look to make it consistent with other approaches.
For example one method would be to build on the existing engineering definitions of Accuracy, Error, Precision, and Uncertainty
However this sort of error analysis alone doesn't tell you much about what is going on in terms of frequency domain analysis, i.e. for sampled measurements resulting in aliasing, phase distortion, frequency response errors, measurement resolution errors etc.
Systematic error from the measurement point of view seems to be analogous to structural uncertainty in the model building point of view i.e. design flaws in the model used.
Random error from the measurement point of view seems to be analogous to parameter uncertainty in the model building point of view. Instead of a measurement error, parameter uncertainty refers to the range of values or likely distribution of values that a model parameter might take.
But whatever the definition you use for the input uncertainty (the nature of the model and its parameter values), you have to be able to relate this uncertainty to the output uncertainty, that is the uncertainty in the numbers coming out of the model. It is these that have to be compared with measured reality. I have no idea what terminology is best for doing this, I expect you will know more about this than me.
I presume that some parameters may be independent of all others and some parameters may correlate with others (i.e. not be independent of others).
I expect you can't just read a text book definitions on this and expect to know a formula that works for every problem you meet. I am not an expert on modelling stochastic systems, so all I am really saying is, try to keep an open mind and give priority to understanding the problem at hand.
When encountering definitions that are confusing, it may mean you are missing something or it may mean that they are somehow incomplete and you have unknowingly started on the path of discovering why.