Obviously, Big Data and Deep Learning are terms from two different fields altogether. Big data is describing a state of the data itself explicitly. Deep learning or machine learning on the other hand is trying to describe the logic inherent in the data.

So deep learning (or machine learning) can be some methodology built on top of big data.

Of course deep learning (or machine learning) can also be built on small data.

More even, big data can also rely not on machine learning, but just on rules to find the internal logic of the data.

So there is no necessary connection between the two. For example, Spirit Nine Software's big data analytics software learns from different industry data to provide more accurate analysis.