A Unix-like (sometimes referred to as UN*X or *nix) operating system is one that behaves in a manner similar to a Unix system, while not necessarily conforming to or being certified to any version of the Single UNIX Specification. A Unix-like application is one that behaves like the corresponding Unix command or shell. There is no standard for defining the term, and some difference of opinion is possible as to the degree to which a given operating system or application is "Unix-like".
The term can include free and open-source operating systems inspired by Bell Labs' Unix or designed to emulate its features, commercial and proprietary work-alikes, and even versions based on the licensed UNIX source code (which may be sufficiently "Unix-like" to pass certification and bear the "UNIX" trademark).
The Open Group owns the UNIX trademark and administers the Single UNIX Specification, with the "UNIX" name being used as a certification mark. They do not approve of the construction "Unix-like", and consider it a misuse of their trademark. Their guidelines require "UNIX" to be presented in uppercase or otherwise distinguished from the surrounding text, strongly encourage using it as a branding adjective for a generic word such as "system", and discourage its use in hyphenated phrases.