Fine-tuning is when you take a pretrained network, change the output layer only, and run the optimizer a little more.

Transfer learning is when you take any sort of pretraining. Fine-tuning is one example of transfer learning. Using pretrained word embeddings is another example of transfer learning.

You can do deep learning without either. It's just that existing pretrained models and components are so good that it's tough to build a competitive model without either.