Turing test we typically define as characteristically human. CAPTCHA is a form of reverse Turing test. Before being allowed to perform some action on a website, the user is presented with alphanumerical characters in a distorted graphic image and asked to type them out. This is intended to prevent automated systems from being used to abuse the site. The rationale is that software sufficiently sophisticated to read and reproduce the distorted image accurately does not exist (or is not available to the average user), so any system able to do so is likely to be a human. Software that could reverse CAPTCHA
Turing completeness is that there exist problems for which it is impossible to predict what a (Turing-complete) system will do over an arbitrarily long time. The classic example is the halting problem: create an algorithm which takes as input (a) a program in some Turing-complete language, and (b) some data to be fed to "that" program; and which determines whether the program, operating on the input, will eventually stop or will continue forever. It is trivial to create an algorithm that can do this for "some" inputs, but impossible to do this in general. For any characteristic of the program's eventual output,