The difference between ‘round’ and ‘around’ is not so definite as it may seem at first. It is not only the fact that ‘round’ is more common for British English and ‘around’ for American. Though both these words can mean ‘movements in circles’, in some cases we can not use them interchangeably.
‘Round’ can be used as a noun, adjective and a verb in a sentence. And these are cases when you can not use ‘around’ instead. For example:
We played another round of golf and left the club.
We bought a beautiful round table.
This website rounded up all the places where you can 'virtually' travel, explore. (WKMG News 6 & ClickOrlando)
‘Around’ is used as an adverb or a preposition to describe the movement or position of the object or a subject. It can mean: on all sides, in a circle, not far away. In all of these cases we can use ‘round’ instead. For example:
We walked around/round the town and had fun.
There is a good cafe around/round the corner.
They have been traveling around/round the world for 3 years.
Jeremy put his hands around/round her waist.
The police worked around/round the clock to catch the burglar. (all day and all night).
But when we need to say ‘approximately’ we can use only ‘around’.
We paid around $300.