Though crème caramel and flan are both creamy custard desserts that are usually flavored and topped with caramel, there are a few factors that separate these dishes.
Crème caramel is a silky and delicate French dessert with a custard base made from milk, eggs, sugar, and vanilla, with a sweet layer of liquid caramel on top.
Crème caramel is assembled in ramekins that are placed into another dish that has been filled with boiling water, then the whole setup is put into the oven and baked.
This cooking technique known as bain-marie is essentially the same as a double-boiler. The top of a crème caramel is sticky and sweet, similar to crème brûlée without a blowtorch.
Flan can be traced back to Ancient Rome, and it's popular in Spanish-speaking countries, the Philippines, and beyond. It can be richer than crème caramel with a spongier texture.
Flan is also shorter and wider in shape than crème caramel. The custard can be baked in many ways, and is served by being flipped upside-down and unmolded from its cooking dish.
Unlike with crème caramel, there are also savory variations on flan that are often flavored with vegetables, and may be baked into a crust and cut into slices like a quiche.