Flat white there are two types. The familiar type we have in Singapore is the aussie version. It is basically latte which is hot milk
without foam. Or at best very little foam. It is basically very liquid with weak texture.
Latte is more foamy, about 2 cm of milk froth on top. The milk itself is also slightly texturised with foam.
Cappuccino is cappuccino. No wet cappuccino or dry cappuccino. Definitely cappuccino is not the Italian name for latte.
Cappuccino is froth till it is like total foam, it appears all foam but after you pour in, a huge part of it becomes back liquid. You put your espresso in. You will see the three layers of froth, milk and espresso almost evenly defined.
Some idiots call dry cappuccino as not good, claim wet cappuccino is correct. Wet cappuccino is basically a latte because the froth on top is only about 2 cm. Cappuccino foam is lighter than espresso, it will float much of the milk on top and not mix as much. Meaning cappuccino is a stronger coffee flavoured drink.
Those that draw exquisite latte art, draw with very fine thickness, are often basically flat whites because it has very thin froth.
Cafe au lait is filtered coffee with French press with milk. Coffee produced with French Press is thicker than kopi because the filter don't hold back the coffee oil as much like socks do but it has more sediment.
