Fat Thursday (Tłusty Czwartek) is the real Pączki Day in Poland. It begins the last six days of carnival called in Polish ostatki. This period of intense partying and food feasting ends in Poland with Śledzik (literally meaning "A Little Herring" - in English referred to as Herring Night), the Polish name for the last Tuesday before Ash Wednesday (the first day of Lent). The name comes from the lean herring dish being served as the harbinger of the upcoming 40 days of fasting.
The Pączki Day in the United States is usually celebrated on Fat Tuesday (or Mardi Grass), called also the Shrove Tuesday. However, the large Polish community in Chicago (IL) celebrates the Pączki Day on both Fat Thursday and Fat Tuesday, while Buffalo (NY) has perhaps the largest Fat Thursday events outside of Poland.
This year Fat Thursday falls on February 11th and Fat Tuesday on February 16th. These dates change every year as they are counted back from the movable date of Easter Sunday that is set depending on the Moon cycles (first Sunday after the first Full Moon occurring on or after the vernal equinox).