The first was lying under oath and obstructing a critically important investigation into consensual oral sex.
The other was obstructing an out-of-control propaganda operation about Russia, and pressuring the government of Ukraine by withholding deadly weapons from its Nazi-aligned war-making government.
Both impeached presidents were acquitted, came out of the process with stronger support than they'd had before, and had zero penalties imposed on them.
This is roughly what most of the U.S. public knows about impeachment, which is why this critical tool of public accountability is in danger of being dismissed by the public.
This is not, in reality, the full story. The U.S. House has impeached 20 officials, including President Andrew Johnson. Eight of them have been convicted in the Senate, three more resigned before they could be, and another was expelled by the Senate and the trial dropped. That's 12 out of 20 effectively dealt with.
Even this is not, in reality, any more than scratching the surface of the full story. The vast majority of impeachment efforts have led to resignations or firings, court rulings, or governmental actions that have resolved to some extent the offenses at issue, prior to achieving an impeachment, much less a conviction. An attorney general like Alberto Gonzales, for example, will typically be forced to resign before impeachment hearings can inform the public about all of his outrages, or about the power of impeachment. But that doesn't mean Gonzales would ever have left without the activist sliver of the public demanding his impeachment.
Even with presidents, the popular story only scratches the surface of what's actually happened. Richard Nixon only left because he was about to be impeached. Harry Truman only lost the power to take over factories because pressure was building to impeach him. John Nichols' book, The Genius of Impeachment, tells some of this history. But Nixon was quite a few years back now. Anybody paying attention knows that every president since could have been impeached for numerous outrages, and that both Clinton and Trump were not impeached for their worst abuses of power.
George W. Bush, who, according to CNN this week, merely "lived through the war on Iraq" (unlike, I would note, over a million of his victims) was a prime candidate for impeachment, as was his vice president. I organized dozens of experts to draft dozens of articles of Bush impeachment for Congressman Dennis Kucinich, who actually introduced a fraction of them (35) into Congress. But Speaker Nancy Pelosi blocked as unimportant an effort that we proponents called preventative, that we swore was about precedent, and that we grimly promised would see similar abuses of power in subsequent presidencies if not acted on.
Barack Obama and Donald Trump predictably expanded on numerous Bush power abuses. But only delusional, racist, rightwing impeachment efforts against Obama got much media attention. Advocates for Trump's impeachment since his inauguration day have long since compiled highlight lists of the most critical articles of impeachment being ignored by the Congress. To take just one topic, Trump has instigated violence against various groups since before his inauguration, including immigrants, blacks, leftists, etc. For Congress to suddenly care only when that violence reaches the halls of Congress is a serious problem, and should tell us all a great deal about who Congress "represents." But it is much better than nothing.
I think finally impeaching a president for a legitimate reason, for a public undisputed act, and for an act that the public wants him impeached for, could seriously help restore the status of impeachment in many people's minds, which could be very good for the future of U.S. government. It could also strip impeachment of numerous slanderous misconceptions. For decades we've been told that any impeachment would take months. The time and work supposedly involved has been a chief argument against numerous impeachments. In vain we have argued back that a vote could be held in 1 day. Now, suddenly, there's been an admission that we were right all along.
Of course, Congress has run screaming from public indisputable actions, in favor of dubious allegations. That has assisted the stalling tactics and evasion of which claims about long impeachments have been part. Trump has openly profited from office, incited violence, interfered with voting rights, discriminated on the basis of religion, waged illegal wars, blown people up with missiles, threatened nuclear wars, pardoned criminals, politicized prosecutions, abused immigrants, neglected those in need, intentionally and openly exacerbated climate collapse, instructed subordinates to break laws, supported coup attempts (in other countries), illegally torn up disarmament treaties, etc., etc., and Congress has preferred unproven allegations about Russia and Ukraine. To finally, at long last, impeach Trump for something he indisputably did would wipe away generations of pretense that an impeachment must be a long obscure investigation, while open power abuses are perfectly permissible.
So, it actually matters that right now we not let Congress get by with just rhetoric or with just the delusional passing of the buck to Mike Pence, or with merely finding some other means of barring Trump from holding future public office. It matters that Pelosi not be allowed to run out the clock on this impeachment. (Pushing the Senate trial into the next Congress and even the next presidency would be fine, and Pelosi fans may feel free to declare it the Genius of Pelosi, but no single person has done more to evade, stall, and sabotage the power of impeachment for decades, so wariness of her delays is always merited.) It matters because a precedent has to be set for presidents who try to overturn elections through fraudulent actions, dishonest demagoguery, and the instigation of violence. It matters because Trump may pardon everyone involved, because he may commit new outrages - even much worse ones, because his successors certainly will if he is given a pass, because if the Biden presidency doesn't start with a serious approach to turning the page it will not deliver anything the world needs, because Trump must be effectively barred from running for office again, because the nonviolent rule of law must reclaim respect now being gained by the increased use of military force in U.S. streets, and for numerous other reasons. But one key reason to impeach is to save the important tool of impeachment from being thrown in the trash.