I think there is no difference.

The size system, whether it be shoe sizes or pants sizes or any other size measurement, is not specific to any particular company. It’s just a standard metric that manufacturers and designers adhere to in order to make the products compatible with one another no matter who makes them. There are many different foot measurements used for sizing shoes around the world, but regardless of what your local measurement might be, you’ll always find the corresponding international sizing for Nike and Adidas running shoes.