Correct me if I am wrong, Overfit is the issue where the train model learns by heart without learning the patterns which affects the test to generalize the data set. If it is so then our train model should not work on the test which implies its a overfit so no need to test further whether its overfit or not. We should straightly go for solving the overfit issue.
That is correct. Overfitting is when your model performs extremely well on the train dataset but not on the test dataset. The following discussion threads might help you get more clarity -
What you really need to know is “bias variance tradeoff”.