To my understanding, you want to know the difference between predictAndUpdateState and Transfer Learning. "predictAndUpdateState" is a function that predicts responses using a trained recurrent neural network and updates the network state, whereas, "transfer learning" is a process where you can take a pre-trained network and use it as a starting point to learn a new task.
You can refer to predictAndUpdateState MathWorks documentation page to learn more on predictAndUpdateState. You can also refer transfer learning using alexnet to MathWorks documentation page to learn more on transfer learning.
