a proper custard is eggs and milk (cooked stove top till it just coats the back of a spoon, then slowly baked in a bane marie till it sets)
but pies like pecan, chess, shoo-fly, pumpkin, coconut and even lemon meringue, (which also has no milk, but lemon juice,water and eggs)are all considered custard type pies. Pumpkin, sweet potato, and coconut pies all do have milk, as well as their title ingredient, but not a lot.
sho-fly pie is a similar custard (to pecan or chess), made with molasses, not corn syrup, and it usally has a crumb topping.
Key lime is also considered a custard type pie, and nowdays, is often cooked, and does have eggs, but originally, it was just sweetened condensed milk, and key lime juice.
(and you can make a caramel custard pie by just baking sweetened condensed milk..no eggs.)
'pudding pies', like black bottom, or mississipi mud pies are consided custard, even when they are made with instant pudding (american style milk puddings)-- are they aren't cooked, and don't have any eggs. these also are some times called cream pies, (especial if they banana instead of chocolate) but a cream usually just means garnished with whipped cream, just as a la mode(in US--i don't know about else where) means "served with ice cream".
our friends in the UK (and perhaps up under) are familiar no doubt with Bird's Custard, a milk custard that is prepared without egg and used as sause, not custard as we americans usually think of custard. any one who is into french cooking would know it as a creme anglais --
I would check a cook book,(Joy of Cooking or other) for a definition of custard, not a dictionary--
(pies are usually classified as custard or non custard. non custard pies are usually fruit pies (and or vegetable, like rhubarb, or savory, like meat pies.)
