Does intentional vomiting do the same damage to your teeth as real vomiting?

Of course, but...: What is present in the vomitus itself is the same stomach acid regardless of whether the emesis was induced or spontaneous. However, if emesis is induced shortly after ingestion of alkaline material or other caustic substances, you may be compounding the damage to your teeth, oral mucosa, airway, esophagus. What motivates you to induce emesis?

Yes: Regurgitation or vomiting exposes your teeth to stomach acids that will erode the tooth enamel if repeated constantly. You must seek help from professionals in the health care field.

Yes: Repetive intentional induction of vomiting will make your teeth extremely susceptible to damage due to the high acid content of the stomach.

Yes and: Rinse vigorously with water after vomiting. Do not brush your teeth for at least 30 minutes as there is often some residual acid present and when combined with tooth brushing will increase the chance of tooth erosions and abrasions. The same is true when you drink sports drinks, many of which are very acidic. Try to get some help for your problem.