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