In Australia and other common law countries like the UK, we use the term Confidentiality Agreement or Confidential Disclosure Agreement. Whereas, in the US the same document is more commonly known as an NDA, or mutual NDA. There is no real difference other than the customary title for the document. To put it poetically, as they say, "a rose is a rose, by any other name".
What makes a Confidentiality Agreement "mutual", I hear you ask?
In most cases, a confidentiality agreement is used when only one of the parties (the disclosing party) intends to share its secrets with the other party (the recipient).
By contrast, a mutual confidentiality agreement is used in a different context. That is, where both parties intend to share confidential information. In this case, the mutual agreement requires both to keep information secret. In other words, it applies equally (or mutually) to both parties.
Let's look at an example, that distinguishes the usual (one way) confidentiality agreement form a mutual (two way) confidentiality agreement.
Let's say you are selling your business. You will likely have confidential information about your customers but it's less likely that the buyer will have anything confidential to hide. Therefore, a one way confidential agreement is reasonable. That is, to protect you but not the buyer.
Now, let's assume the circumstances are different and you plan to merge your business with a business owned by the other party. In this case, both you and the other party will exchange confidential information about your respective customers. Therefore, a two way (mutual) confidentiality agreement is appropriate. It will allow both parties to protect their confidential business information.
If you plan to exchange confidential information (with information flowing both ways), you should put a Mutual Confidentiality Contract in black & white, to protect both parties.
You can use this Agreement to stop people stealing your business information and protect your intellectual property, and at the same time, provide equivalent protection to the other party. This should make them more comfortable dealing with you, knowing that their confidential information is also protected.