What is the difference between a name day and a birth day? Like obviously your birthday is the day you’re born but what is the former?
Okay, so basically: in Catholic and Eastern Orthodox traditions, you have a bunch of saints, and those saints have their feast days (which gave people in the ye olden days reason to parteeee from time to time). And people often got named after saints. So, say, you were named after St. Nicholas. His feast day is December 6. Now that's your nameday.
Of course, over time the tradition totally lost its religious connotations (like, some 20% of Hungary's population is Protestant--at least culturally/coming from a Protestant lineage; the number of people who actively practice their faith is much lower--, and they celebrate their namedays as well). New names came into use (currently, Hungarian is taking over a lot of Anglo-Saxon names, for example), they were... just added to the roster. Like, got assigned a date.
When you buy a calendar in Hungary, it will actually showcase the namedays for every given day, although usually just one or two per day (because of the new names, each day can actually have a bunch of names assigned to it. (Like... my name is Orsolya, and back in the day that was the only form you could have put on the birth certificate, but now some nickname forms, such as Orsi and Orsika are also allowed, so the namedays for those are also celebrated on the "Orsolya" day.) Daily newspapers usually run all the namedays for the day.
Namedays are especially handy in the workplace, for example--your colleagues would not that likely celebrate your birthday, because that'd require asking personal questions, remembering dates, etc. But your nameday? That's on the calendar. In the newspaper.
I kinda celebrate mine, but don't care that much about it? Like, usually I just use it as an excuse to get together with friends and have a couple of drinks.
Fun fact: there are now calendars for pet namedays!