X-ray observations of clusters of galaxies have been used to study the large-scale structure of our Universe and to test cosmological models. In such studies it is critical to understand the unique survey selection function correctly. In comparison to the cluster detection by the Sunyaev-Zel'dovich effect (SZE), it has been shown that X-ray observations preferentially detect clusters that have cool cores or are more relaxed as opposed to more disturbed or non-cool-core clusters found in SZE surveys. In this Letter we show that it is not the means of detection, X-rays or SZE, but the sampling strategy, flux-limited or volume-limited surveying, that makes the difference. XMM-Newton observations of the REFLEX clusters in our Volume-Limited Sample (ReVols) show that the fraction of disturbed clusters, determined by the third moment of the power ratios and by centre shifts, is larger by about a factor of two than that of relaxed clusters. In contrast, two flux-limited cluster samples that can be constructed out of ReVols contain more comparable fractions of disturbed and relaxed clusters, which differ by only ten per cent. We use the ratio of the luminosity measured within r 500 to that measured in the same aperture without the core region as an indicator for a cool core and find that the number of non-coolcore clusters is comparable to or larger than that of the cool-core clusters in ReVols. In addition, we show that the X-ray luminosity distributions of the disturbed and relaxed clusters are distinctly different, and on average, a displacement of 60% in luminosity is required to match two distributions. Therefore the larger fraction of relaxed and cool-core clusters reported in previous X-ray surveys does not result from the X-ray detection per se, but from the fact that these samples were constructed from flux-limited surveys. Our findings also suggest that the Malmquist bias correction used in cosmological studies with X-ray galaxy clusters could be improved by taking the morphological fractions of the galaxy cluster population and their distinct scaling relations into account.