What if the training data and the prediction data are the same?
Yes, it will impact the results.
In the best case your model will not overfit at all so you could expect the same performance between the training set and a previously unseen set (= normally the testing set). In case your model overfits even a little bit, then your results on the training set will be higher (better) than on unseen data.
The impact depends on the classifier/hyperparameters you are testing. For instance, if you are using a KNearestNeighbors classifer with k=1, then the impact will be extreme as you will have 100% accuracy on whatever training set.