On my Antiochian fasting schedule tomorrow is a strict fast day. On a strict fast day you eat nothing for that liturgical day. So depending upon how you see a liturgical day, it would be sundown Sun thru sundown Mon (or after services Monday night if communing), or just all day Monday.Every weekday in Lent is a strict fast. Do you eat nothing all week?
"Strict fast" usually means the same thing as "Lenten fast," which is no meat, dairy, fish, wine or oil. This practice of eating nothing all day on Christmas Eve looks like a local tradition.
Maybe in your parish a strict fast is different? "Strict fast" means eating nothing until the ninth hour or sundown (3pm), and then a single meal which may contain no meat, dairy, eggs, fish, oil, or wine. The regular fasting days of no meat/dairy/wine/oil/fish are just listed as "fasting" days like any other Wed/Fri. The strict fast is reserved for Christmas Eve, and Holy Mon-Thurs. Ideally one would eat their last meal before Pascha Holy Thursday evening. This would be in addition to fasting during the day until the ninth hour. So you would eat "dinner" Holy Mon-Holy Thurs, have a little wine/fruit Saturday evening, then break the fast completely for Pascha. So Holy Mon-Thurs would be listed "strict fast" on the calender, then Holy Fri-Sat is listed "abstain."
There are a number of people that observe the strict fast during Lent as well. They don't eat anything until after the pre-sanctified services during the week.
On our calender is has a little cross on the strict fasting days, the other fasting days are just color coded regular fasting days, then there are days listed as "abstain," and color coded for fasting, for a total fast.
So we have "regular" fasting days, strict fasting days, and abstain days, in addition to the other various combinations of fasting.