Do forgery and fraud mean the same thing?

Forgery: making a false document or other paper, including money.

Fraud: to TAKE something by defrauding or deceiving someone

Simple answer: no, they are not the same. Forgery refers to the act of faking a document to make it look genuine for financial gains. Fraud is tricking someone into giving you money. Forgery is one kind of fraud; there are many others. If you get money by forging someone's signature on a cheque, that is forgery and it is also fraud. If you get people to send you money by sending them an e-mail saying you are an African Prince, it is fraud but not forgery.

Incidentally, fraud and forgery are nouns describing the criminal acts. The verbs are to forge or to defraud.