But what I see is that Speaker Nancy Pelosi is not sitting on the chair -- instead someone else. Why is that? Or is this a different speaker for this purpose? If so, who is she?
"Madam Speaker" is not Rep. Pelosi, but Rep. Diana DeGette, a Democrat from Colorado, who is serving as speaker pro tempore and presiding over the US House of Representatives for the debate on the impeachment of President Trump.
Rules of the House: https://naturalresources.house.gov/imo/media/doc/116-House-Rules-Clerk.pdf
I 8(a): The Speaker may appoint a Member to perform the duties of the Chair. Except as specified in paragraph(b), such an appointment may not extend beyond three legislative days.
... and that's usually exactly what happens. The Speaker wields the gavel on special occasions but on an average day delegates that duty to an underling. While impeachment qualifies, and I would not have been surprised to see her at the podium, she may have been busy whipping votes during the debate.