LGV - Large or Laden goods vehicle. This is the term referring to any vehicle used to transport goods from vans up to articulated lorries.
HGV - heavy goods vehicle. This refers to larger goods vehicles, generally those above 7.5 tonnes for which you need a category C licence, previously called an HGV licence.
MGW - maximum gross weight. It refers to the combined weight of your unladen vehicle, the load on it and any people in it. This is usually on weak bridges to show the heaviest weight the bridge can take.
MAM - maximum authorised mass. This refers to the total combined weight of the vehicle and the maximum load it can carry including people. This is defined by the manufacturer.
Payload. This refers to the total capacity in weight of the load and the people.
HGV class 2 and class 1. These are the old names for Category C and Category C+E respectively.