What does saved classifier actually save?

I am currently in the process of classifying a time series of Landsat scenes using Random Forest. I have used a sample scene to determine the best parameters with my training and testing data. If I choose to apply this saved classifier on my other scenes, is it using the parameters and training vectors from the original classifier or does it use the spectral values? Sorry if this is a bit basic, I just couldn’t find documentation on this anywhere.

You can save a classifier (which was trained on an input dataset) during the first classification and apply it to new data, as long as these new data have exactly the same band names.
It then takes the rules/thresholds derived from your saved classifier and applies them to the new data. From my experience, this does not always work very well because it requires carefully calibrated data which is temporally consistent, and furthermore the result is still very sensitive to the thresholds which might work for the first data but fail to delineate the classes for others. But this also depends on the number of classes, training samples ect. If these are quite robust, it is worth a try.

So in short: The saved classifier no longer uses the training vectors, but the rulesets derived from them in the first classification.