“That’s not exactly how it works. The House tried and convicted Clinton, which is why he is called the impeached president. The Senate assesses penalties and they refused to assess any penalty on Clinton”
This is not true. An impeachment is an indictment, an accusal, not a conviction. The same body would not indict and convict. That would be a violation of common law. It is up to the senate whether the accused is guilty or not guilty of the accusal. In the case of Clinton, they found him not guilty. Should 2/3rds have found him guilty, he would have been removed from office immediately.
Absolutely correct. And, if you read my comment, that's not what I said.
The impeachment is the proceeding. The House conducts the "trial" (if you will) to determine whether there is sufficient evidence to convict. If you recall, in the Clinton case, they found sufficient cause for him to be found guilty of the crime of lying.
It is the Senate's duty to assess the penalty, Again, if you recall from Clinton, the Senate voted along party lines NOT to assess any punishment.
So, we have, essentially, a split decision. The House found sufficient grounds to find the president guilty of lying, but the Senate refused to assess punishment. As a result, Clinton's legacy is still stained with the fact that he was impeached despite the fact that no penalty was assesed.
Should 2/3rds have found him guilty, he would have been removed from office immediately.
Again, not true. Removal from office is an option that the Senate can impose as a penalty, but it is NOT a mandatory sentence to be imposed. There are lesser penalties they can impose if they choose, including censure (which os meaningless).