Are benzocaine and benzodamin hydrochloride the same?

More or less: both are used as topical local analgesics in the oral cavity, read the labels carefully when using either, best wishes

No: Although both medications may be used to relieve pain, each works slightly differently and has different uses. Benzocaine treats pain associated with minor burns, sunburns, minor cuts, and sometimes itchy skin. Benzydamine hydrochloride may be applied as a cream on the skin for muscle pain. It also comes in the form of a mouthwash or a spray to relieve sore throat pain.