Maunday Thursday

[JudgeRightly]

If by "in modern terms" you mean a midnight to midnight calendar day,

YES.

on which night did the Lord's Supper take place - during the first night of Wednesday or during the second night of Wednesday?

After 6pm on Wednesday. Matthew 26:20. The Jewish Calendar date changes at nightfall. They had Supper on 14 Nisan. The start of 13 Nisan was on Tuesday. The start of 14 Nisan was on Wednesday.

Remember? Jesus had to keep waking up his disciples in Gethsemane, and that was after their meal.