We have analysed the differences in positions of 9081 matched sources between the GaiaData Release 2 (DR2) and very long baseline interferometry (VLBI) catalogues. The medianposition uncertainty of matched sources in the VLBI catalogue is a factor of two larger thanthe median position uncertainty in Gaia DR2. There are 9 per cent matched sources withstatistically significant offsets between both catalogues. We found that the reported positionalerrors should be rescaled by a factor of 1.3 for VLBI and 1.06 for Gaia and, in addition, the Gaiaerrors should be multiplied by the square root of chi squared per degree of freedom in order tobest fit the normalized position differences to the Rayleigh distribution. We have establishedthat the major contributor to statistically significant position offsets is the presence of opticaljets. Among the sources for which the jet direction was determined, the position offsets areparallel to the jet directions for 62 per cent of the outliers. Among the matched sources withsignificant proper motion, the fraction of objects with proper motion directions parallel tojets is a factor of three greater than on average. Such sources have systematically higher chisquared per degree of freedom. We explain these proper motions as a manifestation of thesource position jitter caused by flares, which we predicted earlier. Therefore, the assumptionthat quasars are fixed points, and thus that differential proper motions determined with respectto quasar photocentres can be regarded as absolute proper motions, should be treated withgreat caution.