Wheel slips often produce wheel/rail damage, threatening the operation safety, and increasing the maintenance cost of contact-type railways. To understand the characteristics of wheel slips for further development of more accurate slip protection methods, this study employs a validated explicit finite element (FE) method to evaluate the transient wheel-rail rolling/slipping contact behaviors. The contact during the traction of the wheel from both standstill status and moving status is focused. Friction and traction coefficients are the two most crucial factors affecting the wheel slips. Conditions of partial and full slips within the contact patch are determined by setting different combinations of the traction and friction coefficients. The contact behaviors including stick-slip, partial slip, full slip, surface stress, and wear are studied. It is revealed that wheel slips may occur not only in the case where the traction coefficient exceeds the limiting value, but also when being slightly smaller. As a consequence, wheel slips can produce much larger wear-rate. This study provides an insight into the wheel slipping/spinning mechanism and theoretical guidance for the development of more accurate control methods of wheel slips.