The zero-field splitting parameters (ZFSPs), aka magnetic anisotropy (MA) parameters, are crucial for description of transition ions. Compatibility of ZFSPs is indispensable for proper interpretation of experimental and theoretical data. To achieve compatibility of orthorhombic ZFSPs reported for single magnetic 3dN adatoms on surfaces, the distinct nature of ZFS quantities and MA ones, and their interrelationships, are elucidated. The terminological confusion prevalent in adatoms studies results in detrimental consequences, e.g. erroneous values of the true uniaxial MA constant K and/or the axial ZFSP D. It is shown that the intrinsic features of the true orthorhombic ZFSPs: D and E (rhombic) in the conventional notation or B2q (b2q, q=0, 2) in the Stevens notation, bear critically on compatibility of ZFSP sets. Since the standard ZFSP sets (0<λ≡E/D≤1/3) and non-standard ones (λ outside the standard region) belong to disparate regions of the ZFS parameter space, such sets are intrinsically incompatible and cannot be directly compared. The orthorhombic standardization, based on the rhombicity ratio λ≡E/D, is performed to reanalyze the non-standard ZFSP sets identified in recent adatoms studies. The alternative physically equivalent ZFSP solutions that could equally well be obtained by fitting inelastic tunneling spectroscopy (ITS) data or conductance spectra data are provided. Disregarding the intrinsic features may lead to misleading conclusions, e.g. apparently highly rhombic ZFSP set (λ=1) represents actually purely axial case (E≡0). The results enable meaningful comparison of ZFSP data taken from various sources.