Design: To prepare the preliminary sketch or the plans for (a work to be executed), especially to plan the form and structure of.
Develop: To cause to grow or expand.
Designers make the plans, developers execute them.
The output of (UX/Software) designers is not a working system, but rather a blueprint for it.
The output of software developers is a working system.
By way of analogy, architects design, builders develop.
UX and software designers don't build the product - developers do.
Note that sometimes the design is the product, like most of the output of graphic designers. But a system needs someone to build it.