Is “electrocautery” the same thing as Electrosurgery?

No it is not.

Often “electrocautery” is used to describe electrosurgery. This is incorrect. Electrocautery refers to direct current (electrons flowing in one direction) whereas electrosurgery uses alternating current. During electrocautery, current does not enter the patient’s body. Only the heated wire comes in contact with tissue. In electrosurgery, the patient is included in the circuit and current enters the patient’s body.