"and there shall not remain of the flesh that you sacrifice in the evening on the first day until the morning": Which offering do you sacrifice in order to eat it in the evening? This is the chagigah (the festive offering), which is eaten together with the Pesach.
"in the first day until the morning": the morning of the second day.
(Devarim 16:5) "You may not sacrifice the Pesach offering in one …": R. Yehudah says: Whence is it derived that the Pesach is not slaughtered for one (eater)? From "You may not sacrifice the Pesach offering in one."