The panel did cast its first impeachment-related vote on Thursday, but while that action may have drawn attention to their work, it did not change the nature of the probe. The action merely adopted formal procedures to govern the inquiry that was already underway.

So what do the Democrats say they are doing?

Mr. Nadler laid out the committee’s views at the outset of Thursday’s vote on investigative procedures, but only after swatting away some of the questions about its work.

“Some have said that, absent some grand moment in which we pass dramatically from ‘concerned about the President’s conduct’ to ‘actively considering articles of impeachment,’ it is hard to know exactly what the committee is doing here. Others have argued that we can do none of this work without first having an authorizing vote on the House floor.”

Not so, he continued. Nothing in House rules or the Constitution, he said, requires any such action. As long as it is considering articles of impeachment, Mr. Nadler contended, the committee has all the authority it needs to designate that work an impeachment investigation or inquiry.

In the Nixon and Clinton cases, Democrats argue, a House vote was necessary to grant the committee special powers it did not already possess during those periods under the standing rules of the House, like the ability to issue subpoenas and conduct depositions. Under the current House rules, the committee already has all of those authorities.

Mr. Nadler and the lawyers have also pointed to past examples of the House Judiciary Committee acting on its own authority to open inquiries and recommend articles of impeachment against judges and other officials and not drawing any complaints.

Under normal circumstances, the distinction might not matter. It does this time because Democrats have asked for the help of the federal courts to obtain grand jury material related to the special counsel’s Russia investigation and speedily secure the cooperation of witnesses. To get it, they have to convince a judge in the coming weeks that they have met the criteria for an impeachment inquiry.

The list of former Trump administration officials whose testimony the committee is seeking seems to grow by the day; on Friday, an aide confirmed that lawyers have initiated negotiations to get Jeff Sessions, the former attorney general, to appear. Those talks were first reported by The Washington Post.

Republicans and the Justice Department aren’t convinced.

Representative Doug Collins of Georgia, the top Republican on the Judiciary Committee, argued over and over at Thursday’s committee hearing that without a House vote authorizing it, the inquiry is merely regular oversight work dressed up to look more menacing than it is. Democrats were choosing to not formalize their inquiry because they do not have the votes they need to do so, he said.