In India, I am very sure non-IMAX movies are played in IMAX screens. I am not sure whether American IMAX screens plays them. My friend says they "should not" play non-IMAX movies in IMAX screens in America.
Is it true?
IMAX is a brand name. It appears that many cinemas across the world are gearing up to show films on larger-than-average screens under the IMAX banner, without these actually being IMAX-quality films.
There's an article about it here relating to AMC's tie-up with IMAX and showing the difference between a 'classic' IMAX screen and an AMC IMAX screen (see below)
Conversely, most IMAX cinemas in the UK and US regularly run screenings of classic non-IMAX films on their IMAX screens. I myself went to see Akira on an IMAX screen in Birmingham, presumably it had been upscaled to fit the screen without distortion.