Context. For relativistic modeling of high-accuracy astronomical data, several time scales are used: barycentric and geocentric coordinate times (TCB and TCG) and two additional time scales (TDB and TT), which are defined as linear functions of TCB and TCG, respectively.Aims. The paper is devoted to a concise, but still detailed, explanation of the reasons and the implications of the relativistic scalings of astronomical quantities induced by the time scales TDB and TT.Methods. We consequently distinguish between quantities and their numerical values expressed in some units.Results. It is argued that the scaled time scales, the scaled spatial coordinates, and the scaled masses should be considered as distinct quantities that can be expressed themselves in any units and not as numerical values of the same quantities expressed in some different, non-SI units ("TDB units" and "TT units"). Along the same lines, the system of astronomical units is discussed in the relativistic framework. The whole freedom in the definitions of the systems of astronomical units for TCB and TDB is demonstrated. A number of possible ways to freeze the freedom are shown and discussed. It is argued that in the future one should think about converting AU into a defined quantity by fixing its value in SI meters.