The LCV test covers vehicles up to 3500 Kgs gross. This is the test that the majority of commercial vehicles fall into. This test is applicable to most vans and light trucks. If a vehicle can be driven on a category "B" car licence then this is the test you require to tax your vehicle.
The HCV test is for vehicles in excess of 3500 Kgs gross vehicle weight. This is usually truck sized vehicles. Typically this test applies to vehicles which have a tachograph fitted or require a licence type "C1" or "C". Some Jumbo sized vans can also require this test.