No, the Suzuki Burgman and the Suzuki Access 125 do not have the same engine. While both models are scooters manufactured by Suzuki, they have different engines.
The Suzuki Burgman typically comes in two variants: the Burgman Street 125 and the Burgman 200. The Burgman Street 125 is powered by a 124cc single-cylinder, air-cooled engine, whereas the Burgman 200 is equipped with a 200cc single-cylinder, liquid-cooled engine.
On the other hand, the Suzuki Access 125 features a 124cc single-cylinder, air-cooled engine. It is a different engine from the one found in the Burgman models, although they share the same engine displacement.
So, while the Suzuki Burgman Street 125 and the Suzuki Access 125 have similar engine displacements, their engines are distinct and designed specifically for each model.