Here's another distinction from https://www.reference.com/world-view/motion-leave-file-b95d25a2e60d10f0

A motion for leave is a request to file something that is not automatically allowed under the law. Often, a motion for leave to file is used to request a time extension from the court. Once the court receives the motion, the judge may either grant or deny it.

I think SCOTUS is saying to Texas "what are you waiting for, file the motion already!"

The "relief" denied is extra time to get motion in order.

Here's another distinction from https://www.reference.com/world-view/motion-leave-file-b95d25a2e60d10f0

A motion for leave is a request to file something that is not automatically allowed under the law. Often, a motion for leave to file is used to request a time extension from the court. Once the court receives the motion, the judge may either grant or deny it.

I think SCOTUS is saying to Texas "what are you waiting for, file the motion already!"