The definition of impeachment from Wikipedia is:
Impeachment is the process by which a legislative body levels charges against a government official. Impeachment does not in itself remove the official from office; it is the equivalent to an indictment in criminal law, and thus is only the statement of charges against the official.
Wikipedia
On the face of it, it seems Trump has been impeached as that is where the process is at present, but a Bloomberg article sheds more light.
Now that the House of Representatives has voted to impeach President Donald Trump, what is the constitutional status of the two articles of impeachment? Must they be transmitted to the Senate to trigger a trial, or could they be held back by the House until the Senate decides what the trial will look like, as Speaker Nancy Pelosi has hinted?
The Constitution doesn’t say how fast the articles must go to the Senate. Some modest delay is not inconsistent with the Constitution, or how both chambers usually work.
But an indefinite delay would pose a serious problem. Impeachment as contemplated by the Constitution does not consist merely of the vote by the House, but of the process of sending the articles to the Senate for trial. Both parts are necessary to make an impeachment under the Constitution: The House must actually send the articles and send managers to the Senate to prosecute the impeachment. And the Senate must actually hold a trial.
If the House does not communicate its impeachment to the Senate, it hasn’t actually impeached the president. If the articles are not transmitted, Trump could legitimately say that he wasn’t truly impeached at all.
That’s because “impeachment” under the Constitution means the House sending its approved articles of to the Senate, with House managers standing up in the Senate and saying the president is impeached.
As for the headlines we saw after the House vote saying, “TRUMP IMPEACHED,” those are a media shorthand, not a technically correct legal statement. So far, the House has voted to impeach (future tense) Trump. He isn’t impeached (past tense) until the articles go to the Senate and the House members deliver the message.
Once the articles are sent, the Senate has a constitutional duty to hold a trial on the impeachment charges presented. Failure for the Senate to hold a trial after impeachment would deviate from the Constitution’s clear expectation.
For the House to vote “to impeach” without ever sending the articles of impeachment to the Senate for trial would also deviate from the constitutional protocol. It would mean that the president had not genuinely been impeached under the Constitution; and it would also deny the president the chance to defend himself in the Senate that the Constitution provides.
The relevant constitutional provisions are brief. Article I gives the House “the sole power of impeachment.” And it gives the Senate “the sole power to try all impeachments.” Article II says that the president “shall be removed from office on impeachment for, and conviction of, treason, bribery, or other high Crimes and Misdemeanors.”
Putting these three different provisions together yields the conclusion that the only way to remove the president while he is in office is if the House impeaches him and the Senate tries and convicts him.[…]
If the House votes to “impeach” but doesn’t send the articles to the Senate or send impeachment managers there to carry its message, it hasn’t directly violated the text of the Constitution. But the House would be acting against the implicit logic of the Constitution’s description of impeachment.
A president who has been genuinely impeached must constitutionally have the opportunity to defend himself before the Senate. That’s built into the constitutional logic of impeachment, which demands a trial before removal.
To be sure, if the House just never sends its articles of impeachment to the Senate, there can be no trial there. That’s what the “sole power to impeach” means.
But if the House never sends the articles, then Trump could say with strong justification that he was never actually impeached. And that’s probably not the message Congressional Democrats are hoping to send.
Bloomberg