Memorial Day remembers those who died in military service. Veterans Day honors those who have served. Both are occasions to display the flag, but they do not have the same general half-staff instruction.
Memorial Day
The Flag Code specifies half-staff display until noon on Memorial Day, followed by raising the flag to the top. Confirm the local time and any additional applicable order. The day's noon transition is a specific instruction, not the default for every half-staff observance.
Veterans Day
Veterans Day is listed as a day to display the flag. It does not by itself create a general half-staff requirement. A separate applicable mourning order can still overlap with November 11, so check current sources rather than treating the occasion alone as a complete status answer.
A Simple Habit for Either Day
Review the observance guide, check your state, and use the official source for any special instruction. If you follow reminders, choose both the beginning and ending notices so your display reflects the whole observance.
Sources: U.S. Flag Code, 4 U.S.C. 6 and 4 U.S.C. 7; official U.S. government observance information.