Consider this analogy:

A pure chemist discovers a compound with certain novel catalytic properties and publishes the results.

A chemical engineer is working on the problem of storing hydrogen for onboard fuel cells then uses these results to come up with a way to store hydrogen in a non-volatile way.

A computer scientist working in theoretical computer science comes up with a data structure and associated algorithms for sharing files in a network.

A software engineer uses the algorithms to solve a problem in mobile computing.

Just as the pure chemist is not doing chemical engineering, the theoretical computer science is not doing software engineering.