So you say you can impeach a president but not a Senator?
They may not "impeach" in the pure definition, but I do not think it is a clear cut as you state!
The Constitution gives Congress the authority to impeach and remove "The President, Vice President, and all civil Officers of the United States" upon a determination that such officers have engaged in treason, bribery, or other high crimes and misdemeanors. The Constitution does not articulate who qualifies as a "civil officer of the United States"!
Impeachment in the United States - Wikipedia
Keep reading the full article, it is full of interesting examples of what happens to "misbehaving" Senators and other "civil officer of the United States"!