Car auction - private sale or not

[BertBert]

On a well known but not named car auction site (to public, not restricted to trade), there is often the following;

Car registered to company
Car VAT qualifying with VAT invoice provided from company
Private sale - sold by a private individual

Does the invoice actually mean that a company is selling and therefore not a private sale?

[E-bmw]

It is a private sale as they quite rightly say.

It is only NOT a private sale when sold by a garage/car supermarket/dealer etc.