You're right. An emery board is simply a type of nail file - it's cardboard strip with a type of sandpaper glued to it. Other types of nail files are usually metal, but they can be made of other materials.

I've never known that anyone smoothens the top surface of nails O_O

A nail file is used to smooth out or shorten the edges of your nails, but an emery board is used to smoothen the top surface of your nails and give it a shiny look! :)