Lawsuit terminology for the average gun owner

In recent years, state legislatures have passed laws, like New York’s Concealed Carry Improvement Act, that place increasing restrictions on the purchase, possession, and use of firearms. Many such restrictions appear to violate the Second Amendment to the Constitution of the United States, which guarantees that individual citizens’ “right to keep and bear Arms, shall not be infringed.”
Both individuals and organizations have brought lawsuits challenging such laws, but when hunters and shooters try to follow those cases as they move through the courts, they often confront technical and sometimes confusing language that leaves them unsure of what is going on.