Kellyanne Conway, White House adviser, recently dismissed as a “silly semantic argument” questions about President Trump’s use of the word “wall” — is it concrete, steel, see-through, a “smart wall,” slatted, piked, solar-powered, a chain-link fence or just a metaphor?

The semantics, however, are anything but trivial. If the White House and House Democrats are to reach a deal to avert another government shutdown by the Feb. 15 deadline, they must first reach a rough détente over what they are talking about — in particular, the definition of Mr. Trump’s “wall,” and of “border security,” the Democrats’ catchall description of their own approach.

“There’s no magic glossary telling you the difference between a fence and wall or a barrier, they are kind of interchangeable,” said Jeh Johnson, who served as President Barack Obama’s homeland security secretary from 2013 to 2017.

“There is a distinction between governing and political rhetoric, and people should not get trapped in the binary,’” Mr. Johnson said. “The moment when we reach a compromise on the vocabulary is the moment we reach a compromise on the policy.”