'Light railway' and 'Tramways/road' operated under different sets of regulations from each other and 'mainlines'. Today the Light rail transit systems regulations are a development of the earlier (Victorian/Edwardian) legislation.
Historically then.
Light railway is a railway system that is 'fenced' literally, built to a lesser engineering requirement than a 'mainline', and locomotives and rolling stock didn't need special fittings to run on them.
Tramway/road is a railway system that isn't fenced, often runs on the public highway, built to similar/lesser standards than light railways. Tramway locomotives and stock had to be designed so that people and animals etc would be protected from injury by the moving components of the locomotive, wheels, valve gear etc. They would also have strict laws regarding operation such as speeds etc and how they operated on the road, bloke in front with a flag etc etc. eg 'modern' 50's/60's variants here
c.08/1970 - Norwich Thorpe TMD. | Flickr - Photo Sharing!
NB rear loco is 'tramway' version.
The Brill branch IIRC statred as a tramway, then was 'upgraded' to light railway status to allow more powerful locomotives to operate in anticipation of increased traffic levels and the area expanding into 'Metroland' for commuting John Betjeman styley. For you 'Oxon' types, have a look for 'The Wantage Tramway', another one of Englands bucolic yet iconic light railways.