Geomagnetic storms and substorms play a central role in both the daily life of mankind and in academic space physics. The profiles of storms, especially their initial phase morphology and the intensity of their substorms under different interplanetary conditions, have usually been ignored in previous studies. In this study, 97 intense geomagnetic storms (Dstmin ≤ –100 nT) between 1998 and 2018 were studied statistically using the double superposed epoch analysis (DSEA) and normalized superposed epoch analysis (NSEA) methods. These storms are categorized into two types according to different interplanetary magnetic field (IMF) Bz orientations: geomagnetic storms whose IMF is northward, both upstream and downstream relative to the interplanetary shock, and geomagnetic storms whose upstream and downstream IMF is consistently southward. We further divide these two types into two subsets, by different geomagnetic storm profiles: Type I/Type II — one/two-step geomagnetic storms with northward IMF both upstream and downstream of the interplanetary shock; Type III/TypeIV — one/two-step geomagnetic storms with southward IMF both upstream and downstream of the interplanetary shock. The results show that: (1) geomagnetic storms with northward IMF both upstream and downstream of the interplanetary shock have a clear initial phase; geomagnetic storms with southward IMF in both upstream and downstream of the interplanetary shock do not; (2) the IMF is an important controlling factor in affecting the intensity characteristics of substorms. When Bz is positive before and after the interplanetary shock arrival, the Auroral Electrojet (AE) index changes gently during the initial phase of geomagnetic storms, the median value of AE index is maintained at 500–1000 nT; (3) when Bz is negative before and after the interplanetary shock arrival, the AE index rises rapidly and reaches its maxmum value about one hour after storm sudden commencements (SSC), although the time is scaled between reference points and the maximum value of AE is usually greater than 1,000 nT, representing intense substorms; (4) for most cases, the Dst0 usually reaches its minimum at least one hour after Bz. These results are useful in improving contemporary space weather models, especially for those that address geomagnetic storms and substorms.