Cation-ordered Li[Ni1/2Mn3/2]O-4 with a P4(3)32 space group (CO-LNMO) and "cation-disordered'' (CDO) LNMO are thought to be the state-of-the-art materials for lithium-ion batteries. However, in contrast to CO-LNMO, the crystal structure and electrochemical reaction scheme of CDO-LNMO are not fully understood. We have measured the muon-spin rotation and relaxation (mu SR) spectra for samples of both CO-LNMO and CDO-LNMO, in particular at their magnetic transition temperatures (T-C) below 130 K. The weak transverse field (wTF) mu SR measurements reveal that the range of T-C for the CDO-LNMO sample is very large (Delta T-C similar to 55 K) compared with that for the CO-LNMO sample (Delta T-C < 5 K). This suggests an inhomogeneous cation distribution in the CDO-LNMO sample, because the sample consists of multiple phases with different T-C. Based on the wTF-mu SR result for stoichiometric LiMn2O4, we have proposed that CDO-LNMO is a mixture of L[Ni1/2-omega Mn3/2+omega]O-4 and LiMn2O4.