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We study a sample of 16 Type Ia supernovae (SNe Ia) having both spectroscopic and photometric observations within 2 $-$ 3 days after the first light. The early $B-V$ colors of such a sample tends to show a continuous distribution. For objects with normal ejecta velocity (NV), the C~II $λ$6580 feature is always visible in the early spectra while it is absent or very weak in the high-velocity (HV) counterpart. Moreover, the velocities of the detached high-velocity features (HVFs) of Ca~II NIR triplet (CaIR3) above the photosphere are found to be much higher in HV objects than in NV objects, with typical values exceeding 30,000 km~s$^{-1}$ at 2 $-$ 3 days. We further analyze the relation between %velocities of Si~II~$λ$6355 at maximum, $v_{\rm Si,max}$, the velocity shift of late-time [Fe~II] lines ($v_{\rm [Fe~II]}$) and host galaxy mass. We find that all HV objects have redshifted $v_{\rm [Fe~II]}$ while NV objects have both blue- and redshifted $v_{\rm [Fe~II]}$. It is interesting to point out that the objects with redshifted $v_{\rm [Fe~II]}$ are all located in massive galaxies, implying that HV and a portion of NV objects may have similar progenitor metallicities and explosion mechanisms. We propose that, with a geometric/projected effect, the He-detonation model may account for the similarity in birthplace environment and the differences seen in some SNe Ia, including $B-V$ colors, C~II feature, CaIR3 HVFs at early time and $v_{\rm [Fe~II]}$ in the nebular phase. Nevertheless, some features predicted by He-detonation simulation, such as the rapidly decreasing light curve, deviate from the observations, and some NV objects with blueshifted nebular $v_{\rm [Fe~II]}$ may involve other explosion mechanisms.