(A) round and about

1 circular movement etc

In British English, we usually use round for movement or position in a circle or a curve.

She walked round the car and looked at the wheels.

We all sat round the table.

'Where do you live?' 'Just round the corner.'

2 touring; distribution

British people also use round to talk about going to all (or most) parts of a place, or giving things to everybody in a group.

We walked round the old part of the town.

Can I look round?

Could you pass the cups round, please?

3 indefinite movement and position

We use around or about to refer to movements or positions that are not very clear or definite: 'here and there', 'in lots of places', 'in different parts of, 'somewhere in' and similar ideas.

The children were running around/about everywhere.

Stop standing around/about and do some work.

'Where's John?' 'Somewhere around/about'

I like doing odd jobs around/about the house. We also use these words to talk about time-wasting or silly activity.

Stop fooling around/about. We're late. And around/about can mean 'approximately', 'not exactly'.

There were around/about fifty people there.

'What time shall I come?' 'Around/About eight'

American English

Note that in American English, about is mostly used to mean 'approximately', 'not exactly'; for the other meanings discussed in 1-3, Americans normally use around.