Context. Orion-KL is a remarkable, nearby star-forming region where a recent explosive event has generated shocks that could have released complex molecules from the grain mantles. Aims. A comparison of the distribution of the different complex molecules will help in understanding their formation and constraining the chemical models.Methods. We used several data sets from the Plateau de Bure Interferometer to map the dimethyl ether emission with different arcsec spatial resolutions and different energy levels (from E up = 18 to 330 K) to compare with our previous methyl formate maps. Results. Our data show remarkable similarity between the dimethyl ether (CH 3 OCH 3 ) and the methyl formate (HCOOCH 3 ) distributions even on a small scale (1.8 × 0.8 or ∼500 AU). This long suspected similarity, seen from both observational and theoretical arguments, is demonstrated with unprecedented confidence, with a correlation coefficient of maps ∼0.8. Conclusions. A common precursor is the simplest explanation of our correlation. Comparisons with previous laboratory work and chemical models suggest the major role of grain surface chemistry and a recent release, probably with little processing, of mantle molecules by shocks. In this case the CH 3 O radical produced from methanol ice would be the common precursor (whereas ethanol, C 2 H 5 OH, is produced from the radical CH 2 OH). The alternative gas phase scheme, where protonated methanol CH 3 OH + 2 is the common precursor to produce methyl formate and dimethyl ether through reactions with HCOOH and CH 3 OH, is also compatible with our data. Our observations cannot yet definitely allow a choice between the different chemical processes, but the tight correlation between the distributions of HCOOCH 3 and CH 3 OCH 3 strongly contrasts with the different behavior we observe for the distributions of ethanol and formic acid. This provides a very significant constraint on models.