What's the difference between a New York Egg Cream and a Philadelphia Egg Cream?

And here I always thought an egg cream was an egg cream. The egg cream (a milkshake made from milk, chocolate syrup and seltzer/soda water) is generally thought to have originated in New York City near the end of the 19th century.

https://en.wikipedia.org/wiki/Egg_cream

Apparently, there is a Philadelphia store that sells their personal variant, which has the cream and egg so famously missing from the original recipe!

We went for the best egg cream in Philadelphia and found not one but two. The New York style was perfect done as I remembered as a child in chocolate. The Philadelphia style was new to me with heavy cream and real egg in chocolate as well.

https://www.tripadvisor.com/LocationPhotoDirectLink-g60795-d629008-i48972463-Franklin_Fountain-Philadelphia_Pennsylvania.html

The New York Egg Cream has no eggs, and no cream. The so-called Philadelphia Egg Cream contains both eggs and cream.

The following is from page 16 of a menu from the Franklin Fountain in Philadelphia.

New York Egg Cream...

Does our New York Egg Cream use Fox's? U-Bet it does. No egg, no cream.

Philadelphia Egg Cream...

A recipe for "Egg Cream" appears on page 112 listing as the ingredients: Cream, {simple} Syrup, Vanilla extract, {Raw} Egg yolks. We call this a "Philadelphia Egg Cream." You decide which is richer: New York or Philadelphia.

http://www.franklinfountain.com/wp/FFMenus/FF-menu-web.pdf