Integrated on-board battery chargers (OBCs) have been recently introduced as an optimal/elegant solution to increase electric vehicle (EV) market penetration as well as minimize overall EV cost. Unlike conventional off-board and on-board battery chargers, integrated OBCs exploit the existing propulsion equipment for battery charging without extra bulky components and/or dedicated infrastructure. OBCs are broadly categorized into three-phase and single-phase types with unidirectional or bidirectional power flow. This paper starts with surveying the main topologies introduced in the recent literature employing either induction or permanent magnet motors to realize fully integrated slow (single-phase) and fast (three-phase) on-board EV battery charging systems, with emphasis on topologies that entail no or minimum hardware reconfiguration. Although, permanent magnet (PM) motors with conventional double-layer distributed winding layouts have been deployed in most commercial EV motors, the non-overlapped fractional slot concentrated winding (FSCW) has been the prevailing choice in the most recent permanent magnet motor designs due to its outstanding operational merits. Hence, a thorough investigation of the impact different FSCW stator winding designs have on machine performance under the charging process is presented in this paper. To this end, the induced magnet losses, which represent a challenging demerit of the FSCW, have been used to compare different topologies under both propulsion and charging operation modes. Based on the introduced comparative study, the optimal slot/pole combinations that correspond to the best compromise under both operational modes have been highlighted.