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An axion is a proposed elementary particle, which would explain some experimental results in particle physics, and could comprise cold dark matter (CDM) (or warm or perhaps most likely, hot). The axion was theorized in 1977 to fill out the standard model of particle physics to resolve the strong CP problem, i.e., explaining why the strong force never violates CP symmetry, a symmetry which is never seen violated, but no reason is known why. They would be a dark matter candidate if they exist and have mass. Some fuzzy dark matter models suggest dark matter (or some of it) consists of ultra-light axions, orders-of-magnitude less massive than any known particle.
The term axion-like particle (ALP) has been used for theorized low-mass particles, but without specifically presuming they are axions, i.e., without presuming they resolve the strong CP problem. The term has been used, for example, for a fuzzy dark matter particle (with sufficiently low mass) that doesn't happen to solve the strong CP problem.