WASHINGTON — From his office on the first floor of the Capitol on Wednesday, the second-ranking House Democrat, Representative Steny H. Hoyer of Maryland, was unequivocal: An impeachment investigation of President Trump is not underway.

Over in the Rayburn Building, the chairman of the House Judiciary Committee, Representative Jerrold Nadler of New York, has been hard at work at what he says is exactly that.

And while she moved briskly through the corridors of Congress this week, House Speaker Nancy Pelosi seemed to navigate somewhere in between, reiterating a kind of mantra — “legislate, investigate and litigate” — that seems tailor-made to avoid the “i” word.

As their investigations of Mr. Trump enter a new phase after six weeks away from Washington, Democrats from all corners of the House are finding it increasingly difficult to agree on how to label just what it is that they are up to in building a case against the president — particularly when it comes to the politically charged and constitutionally weighty term “impeachment.”