Less like the other capability models than just about anything else, and thereby a terrible choice of name. By the matrix in CapabilityMythsDemolished, the AccessControlList model actual has more in common with the original capability model (now called the ObjectCapabilityModel) than does PosixCapabilities.

When people refer to the "capabilities" built into the Linux OS, they are referring to the capabilities of the PosixStandard.

See http://wt.xpilot.org/publications/posix.1e/ 

This is the definition of Posix.1e taken from the standards paper: 

Abstract: IEEE Std 1003.1e is part of the POSIX series of standards. It defines security interfaces to open systems for access control lists, audit, separation of privilege (capabilities), mandatory access control, and information label mechanisms. This standard is stated in terms of its C binding. 

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CapabilityMythsDemolished CapabilitySecurityModel