model evaluation with "train_test_split" not static?
You can set random_state parameter to some constant value to reproduce data splits. On the other hand, it's generally a good idea to test exactly what you are trying to know - i.e. run your training at least twice with different randoms states and compare the results. If they differ a lot it's a sign that something is wrong and your solution is not reliable.
According to the resources online "train_test_split" function from sklearn.cross_validation module returns data in a random state. 
Does this mean if I train a model with the same data twice, I am getting two different models since the training data points used in the learning process is different in each case?
In practice can the accuracy of such two models differ a lot? Is that a possible scenario?