I think that if you break the key stages involved in UX Design (and these are not necessarily in any specific order), you have the Research, Design, Prototype and Test that we typically associate with any user-centric and design thinking processes. But these are methodologies that one follows once the way that the project is to be carried out has been determined.
So who exactly determines what the approach/strategy that should be taken for any given project or team? I think that's where you'll find the term UX strategy comes into the picture.
A long time ago, when there were roles like UX Architect (this is probably showing my age), it was the responsibility of your one-man UX shop to figure out how to do the UX design work and then execute it. This is the separation between Strategy and Execution. Strategy is the planning and management of the work, while the execution is the delivery of that work.
Nowadays, with bigger teams and more complex projects, often it will be the role of the Head of / Lead / Senior UX Designer to plan the work, while the more junior UX Designers carry out the work that has been planned.
Even though you could essentially apply the same process to do the strategy design work (i.e. research, design, prototype, test) as you can with the UX design work, the output or the artefacts will be considerably different because when you do the strategy work it is about creating a plan that can help deliver the team and process required, whereas the execution work is about delivering a product or service (and that's where the UX or Service Designer comes in).