Not so. When the Senate “tries an impeachment”, Senators render their judgment by voting “guilty” or “not guilty”. The Senate isn’t part of the judicial branch, and the maximum sentence it can render is removal from office and disqualification to hold office in the future.
Nevertheless, an impeachment trial is one type of trial, described as such in the Constitution, and if Senators obey their oath to “do impartial justice according to the Constitution and laws”, it is most definitely about guilt or innocence.
Strictly speaking, that’s true. Even if he had been removed by the Senate, I would not describe him as “guilty of perjury” on that basis alone. Those words would imply a judicial verdict finding him guilty of a specific violation of a specific federal perjury law. Rather, I would describe him as having been found guilty of an article of impeachment alleging perjury.
By this time, I’m no longer sure what we’re arguing about. The first article of impeachment accused Clinton of providing “perjurious, false, and misleading testimony”, and on that basis, it’s proper to say that he was impeached for perjury.
He may have been as innocent as the mountain air, and the charge may have been political grandstanding at its worst. Nevertheless, he was impeached on a charge of perjury.