This article presents the results of the application of the new measurement standards for teleseismic magnitudes. They have been applied in parallel with traditional Chinese magnitude procedures to more than 14,000 digital broadband-velocity seismograms of 531 earthquakes in the magnitude range 4–9. The records were made between 2001 and 2007 at stations of the China National Seismographic Network (CNSN) and analyzed at the China Earthquake Network Center (CENC). The regression relations between different types of standard magnitudes, traditional Chinese magnitudes, and the respective values of mb, MS, and Me published by the National Earthquake Information Center (NEIC), as well as Global Centroid Moment Tensor (GCMT) moment magnitudes Mw, are presented. The new broadband body-wave magnitude mB(BB) is measured at dominant periods in the range 0.2<T<30 sec that on average increase exponentially with magnitude, as expected by seismic scaling laws. The broadband surface-wave magnitude MS(BB) measures the maximum Rayleigh-wave amplitudes in a wide range of periods (3≤T<60 sec) and epicentral distances (2°≤Δ≤160°), as originally proposed for the current International Association of Seismology and Physics of the Earth’s Interior (IASPEI) standard calibration function for MS determination. The article analyzes and disproves with rich data several widespread prejudices or misunderstandings concerning the applicability, stability, and accuracy of magnitudes based on readings from unfiltered broadband records in general and the IASPEIMS formula in particular. It is shown that the use of surface-wave amplitudes in a broad period range removes most of the systematic distance dependence that is observed when the IASPEI formula is restricted to periods around 20 sec. In the distance range between 2° and 103°, we have investigated the trend between MS(BB) and MS(20), which is the common surface-wave magnitude determined by the NEIC for periods between 18 and 22 sec and at teleseismic distances only. The two magnitudes agree rather well and have comparable measurement errors, even when MS(BB) is measured at regional distances of less than 20°. On average, however, MS(BB) is slightly larger than MS(20) at distances less than 45° with a small and consistent distance-dependent trend in the residuals MS(BB)-MS(20) of -0.0029 magnitude units per degree in both the regional and teleseismic distance range. The analyzed regression relations further reveal the following: (1) the new standard for mb delays saturation and yields about 0.5 units larger mb values for great earthquakes; (2) broadband mB(BB) moves the saturation limit for body-wave magnitudes further up to about 8.3. This makes mB(BB) a good candidate for providing rapid magnitude estimates of strong earthquakes well ahead of Mw; (3) standard MS(20) scales perfectly with the MS published by the NEIC; (4) MS(BB) reduces the underestimation of surface-wave magnitude by MS(20) for weaker earthquakes and those recorded at regional distances for which the maximum surface-wave amplitudes occur mostly at periods well below 16 sec; and (5) new mB(BB) and MS(BB), that is, the body-wave and surface-wave magnitudes directly measured on velocity-broadband records, reproduce well the classical Gutenberg–Richter relation between mB and MS, which—together with the relation between seismic energy ES and mB—formed the basis for deriving the modern moment- and energy-magnitude scales Mw and Me.