Grayware (or PUA - a Potentially Unwanted Application) is a broad category of software, whose intent is not as unequivocally malicious as with other types of malware, such as viruses or trojan horses. It may however install additional unwanted software, change the behavior of the digital device, or perform activities not approved or expected by the user.
Categories that may be considered grayware include: adware, spyware, various browser toolbars, rogue software, bundleware, trackware, or any other borderline software, or software that uses illicit or at least unethical business practices (despite appearing legitimate) and might be deemed undesirable by an end user who became aware of what the software would do if allowed to install.
A Possibly Unsafe Application is one that is in itself legitimate (possibly commercial) software but which might be misused by an attacker. Detection of these types of application can be enabled or disabled by users of ESET software.
For further details on these kinds of software, refer to the whitepaper Problematic, Unloved and Argumentative: What is a potentially unwanted application (PUA)?