There was only one Bessie but she underwent several modifications.
On screen, these were performed by the Doctor.
Off screen, they were done by the Special Effects team and a company called Gluntura Plastics.
Gluntura Plastics made the most extensive modifications, after Bessie had suffered a series of breakdowns during the making of Season 10. This was almost a complete rebuild, including a new bonnet (hood, to US readers) and nose, to accommodate a larger engine. That's probably why she looked like a different vehicle.