If you've trained it with a set of data, A, it's holding it's learned values somewhere - where, depends on your code.
Theoretically, if you moved the algorithm without its learned values to a new place, and retrained it with the same set of data, it should learn the same set of values again. (Whether it does or not is somewhat dependent on how you select initial values)
That said, the Algorithm determines how the Model sets its values (or adjusts them with new data), the Model should be carrying around the values somewhere, and should save those values between executions of the model. (If Pixel6 < 200, then Result = Yes, for example, is an extremely simple model.)
A model doesnt learn anymore - it takes input, and spits out output. If i send the same image through a model 1000 times, it gives me the same answer every time.
If you take the results of a model, give it the correct values ("Was this a face? Yes/No), and run the additional set of data through the Algorithm, you generate a new Model, with slightly different values. (I take the input from my model, and tell if that such and such was NOT a face. Now running that data through the algorithm generates a model such that If Pixel6 < 190 then Result = Yes)