sklearn method model.fit(x---, y--)
model.fit(X, y) doesn't explicitly give you the score, if you assign a variable to it, it stores all the artifacts, training parameters. You can get the score by using model.score(X, y).
Overfitting in simple words is increasing the variance in your model by which your model fails to generalize. There are ways to reduce overfitting like feature engineering, normalization, regularization, ensemble methods etc.
I have a question regarding the model.fit method and overfitting from the scikit learn library in Pandas
Does the generic sklearn method model.fit(x---, y--) returns the score after applying the model to the specified training data?
Also, it is overfitting when performance on the test data degrades as more training data is used to learn the model?