All programmers are language designers and there is actually no distinction between programming and language design. This peculiar belief that there is a distinction is the root of most of the most serious problems in this industry.
But if you try to invent your own language (like Tolkien did), you are not "expressing an idea" (aka: speaking), you are creating a framework to express ideas.
When you write a program, you follow a grammar to express an idea (the solution to the problem you are tackling). When you design a programming language, you are creating that grammar (using another language to implement it afterwards).
Also, here "programming language designers" designates "people who are working on their own programming language". Those are the people I'm talking to when writing this Rust crate and blog article. The webdev doing CRUD microservices could not care less about astmaker.