No, they are similar, but they are not the same. Automobile engineering and automotive engineering are both branches of engineering. Automobile engineering deals with cars in particular.

Automobile engineers design cars, design the engines and fuel capacities. Automotive engineering deals with devising the plan and procedure of making vehicles. It starts with envisioning an idea, to making it, and then testing it.

Both the fields are closely related. Often, people get confused between the two.