This paper performs a first wideband indoor channel measurement at the 105 GHz sub-terahertz (sub-THz) band and analyzes the multipath characteristics in terms of the omnidirectional path-loss and angular characteristics. The measurement campaigns with the 4 GHz bandwidth are performed focusing on indoor short-range communication scenarios in a conference room, corridor, and office room, which have been considered in the primary 60 GHz communication systems standardized by the IEEE 802.15.3c/11ad. Moreover, to draw full understanding to scale the 60 GHz indoor channel models and 60 GHz system designs for the 105 GHz band, we also conduct 60 GHz channel measurements in the same environment with few modifications in the channel-sounding system and performed the comparison between these two bands. Based on these measurements, we demonstrate the affinity that exists between 105 GHz and 60 GHz bands in terms of path loss exponent and angular characteristics of multipath components, shedding light on the hypothesis that several system designs of the 60 GHz communication systems (e.g., beam switching for non-line-of sight conditions) can be applied to the 105 GHz sub-THz communication systems.