After I instantiate a scikit model (e.g. LinearRegression), if I call its fit() method multiple times (with different X and y
You can use term fit() and train() word interchangeably in machine learning. Based on classification model you have instantiated, may be a clf = GBNaiveBayes() or clf = SVC(), your model uses specified machine learning technique.
And as soon as you call clf.fit(features_train, label_train) your model starts training using the features and labels that you have passed.
you can use clf.predict(features_test) to predict.
If you will again call clf.fit(features_train2, label_train2) it will start training again using passed data and will remove the previous results. Your model will reset the following inside model:
You can use partial_fit() method as well if you want your previous calculated stuff to stay and additionally train using next data