In case you were curious, in America, we don't use either of these terms, both jobs as described by Mark would be called a 'traffic cop' in everyday American English

There is a slight difference. Traffic wardens were common and they issue tickets for parking violations. Traffic stewards legally have the power to control traffic and to request names and addresses for road traffic offences. The traffic warden role is being phased out in most parts of the U.K with responsibility to enforce parking violations with local councils or police volunteers.