There are some common sizes and yes, they depend. It's not really about which side of whatever ocean you're from, but rather about what factory you make them in. For example, if you ask a factory that produces a 60x42 cm board (random values, here!), they will have these settings in their printing, cutting and folding machines. They will probably accept if you ask for a 59x43 cm board, but it will cost you more.
If you intend to make a game of your own and build it with cardboard and duct tape, there is absolutely no standard. I've never heard a player saying "That board could use 1 more centimeter in width".
As for the box, things get a little bit more tricky. Because boxes are to be aligned in the shelf (at the shop or at home). Having different sizes means playing Tetris to put them all in place. A very interesting discussion that took place on BoardGameGeek will tell you about the boxes and the standards linked to each manufacturer. Yes, you got it! That depends on the manufacturer!
Again, if you intend to create a new brand and flood the market with tons of your games, you could choose whatever size you like, that will be your standard. Just remember what XKCD said about standards…