Deep learning is a subset of machine learning methods based on artificial neural networks that learn from large amounts of data. We refer to ‘deep learning’ because the neural networks have various (deep) layers that enable learning.
Smart learning is a general term for education in today's digital age that is concerned with context-aware ubiquitous learning. Smart learning environments are technology-supported learning environments that implement adaptations and provide appropriate support in the right places and at the right time based on the needs of individual learners.
Deep learning is a subset of machine learning methods based on artificial neural networks that learn from large amounts of data. We refer to ‘deep learning’ because the neural networks have various (deep) layers that enable learning.
Smart learning is a general term for education in today's digital age that is concerned with context-aware ubiquitous learning. Smart learning environments are technology-supported learning environments that implement adaptations and provide appropriate support in the right places and at the right time based on the needs of individual learners.
It must be emphasized, that these terms belong to different areas of knowledge. Deep learning is a term from the field of ML in AI, a technology when machines can learn by themselves. This trend has been evolving since at least the 1980s. These methods essentially depend on the power of computing systems and develop in direct dependence on these, espessially this develop for artificial neural network. It should be noted that the information in the first link of Arianna D'Ulizia's answer is not scientific, but popular. If only because there is not a citations. In fact, there are many publications, both general and partial.
Smart learning it is term from pedagogy/education. This is concept of Smart learning, firstly apllied in Malaysia (in end of 1990s). Now it is quite a respectable market direction in education. There are quite enough scientific and scientific-like speculations (see, for example, the citations in second link, given by Dr. Arianna D'Ulizia).
Deep learning refers to the new addition to Machine learning that draws it closer to achieving one of its primary objectives which is attaining artificial intelligence with machines. Smart learning on the other hand refers to a teaching and learning technique that involves delivering lessons to students through their mobile devices especially smart phones,IPADS and laptops