Data structures and algorithms existed before any particular implementation, and they continue to exist independently of any particular implementation, such as the C++ STL.
You can study data structures from several points of view:
- What are the main data structures, what are their properties, and in what circumstances each of them is typically used.
- How these data structures are implemented, and why they satisfy the stated properties.
- Limits on data structures.
As a user of data structures, you are mostly interested in the first point. Introductory courses on data structures typically contain a mix of the first two points, with perhaps a sprinkling of the third one (lower bound on comparison-based sorting).
As a programmer, you also need to be aware of software libraries implementing various data structures, but this should be easy to pick up if you understand the underlying data structures themselves.