Originally posted by @mott-the-hoople
no one is removed because they were impeached. Impeach simple means to indict.
Impeach/indict is just deeming a case worthy of trial.
http://www.heritage.org/constitution/#!/articles/1/essays/11/impeachment
Yes, those impeached must be convicted as well. But it has been established since 1798 that the impeachment process does not apply to members of Congress, so Waters is correct:
a U.S. Senator (William Blount of North Carolina in 1797) have also been impeached.
Blount’s impeachment trial—the first ever conducted—established the principle that Members of Congress and Senators were not “Civil Officers” under the Constitution, and accordingly, they could only be removed from office by a two-thirds vote for expulsion by their respective chambers. Blount, who had been accused of instigating an insurrection of American Indians to further British interests in Florida, was not convicted, but the Senate did expel him.
http://history.house.gov/Institution/Origins-Development/Impeachment/
I do not agree the article you cited conclusion that because the House has the sole power of impeachment it can impeach for anything it pleases and the judiciary cannot review it. Article II, Section 4 clearly gives provides: "“The President, Vice President and all Civil Officers of the United States, shall be removed from Office on Impeachment for, and Conviction of,
Treason, Bribery, or other high Crimes and Misdemeanors.” and Article III just as clearly states: "Section 2.
The judicial power shall extend to all cases, in law and equity,
arising under this Constitution,
In theory, if the House choose to impeach someone for reasons not amounting to "Treason, Bribery, or other high Crimes and Misdemeanors" or impeach someone not a "civil official of the United States" the aggrieved party would have a case in that arose under the Constitution and thus within the judicial power of the United States.