The 2D scaling properties of GaN surfaces have been studied by means of the 2D height-height correlation function (HHCF). The GaN layers under investigation presented exemplar morphologies, generated by distinct growth methods: a molecular beam epitaxy (MBE) grown surface decorated by hillocks and a metal organic vapor phase epitaxy (MOVPE) grown surface with terraced structure. The 2D statistical analysis of these surfaces has allowed assessing quantitatively the degree of morphological variability along all the different directions across each surface, their corresponding roughness exponents and correlation lengths. A scaling anisotropy as well as correlation length anisotropy has been detected for both hillocked and terraced surfaces. Especially, a marked dependence of correlation length from the direction across the terraced surface has been observed. Additionally, the terraced surfaces showed the lower root mean square (RMS) roughness value and at the same time, the lower roughness exponent value. This could appear as a contradiction, given that a low RMS value is associated to a smooth surface, and usually the roughness exponent is interpreted as a "measure" of the smoothness of the surface, the smoother the surface, the higher (approaching the unity) is the roughness exponent. Our case study is an experimental demonstration in which the roughness exponent should be, more appropriately, interpreted as a quantification of how the roughness changes with length scale. (C) 2018 Elsevier B.V. All rights reserved.