Blazars are usually classified following their synchrotron peak frequency ($ u F( u)$ scale) as high, intermediate, low frequency peaked BL Lacs (HBLs, IBLs, LBLs), and flat spectrum radio quasars (FSRQs), or, according to their radio morphology at large scale, FR~I or FR~II. However, the diversity of blazars is such that these classes seem insufficient to chart the specific properties of each source. We propose to classify a wide sample of blazars following the kinematic features of their radio jets seen in very long baseline interferometry (VLBI). For this purpose we use public data from the MOJAVE collaboration in which we select a sample of blazars with known redshift and sufficient monitoring to constrain apparent velocities. We selected 161 blazars from a sample of 200 sources. We identify three distinct classes of VLBI jets depending on radio knot kinematics: class I with quasi-stationary knots, class II with knots in relativistic motion from the radio core, and class I/II, intermediate, showing quasi-stationary knots at the jet base and relativistic motions downstream. A notable result is the good overlap of this kinematic classification with the usual spectral classification; class I corresponds to HBLs, class II to FSRQs, and class I/II to IBLs/LBLs. We deepen this study by characterizing the physical parameters of jets from VLBI radio data. Hence we focus on the singular case of the class I/II by the study of the blazar BL Lac itself. Finally we show how the interpretation that radio knots are recollimation shocks is fully appropriate to describe the characteristics of these three classes.
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