I asked the same question this year. My wife's family is all about boiled custard and they serve it as a beverage
with the dessert. I am not a fan (too sweet). To me, it tastes like melted french vanilla ice cream.
Apparently, eggnog is a simple mixture whereas boiled custard is actually cooked? Eggnog is considered a beverage and is usually thinner in consistency, usually contains a spice like nutmeg and is more often used as a vehicle for alcohol. They told me the two are nothing alike, but damned if I can tell a difference.