St link v2 and stm32f401rbt
Both stm32f103 and stm32f401 have the SWD, so you should be able to use the ST-Link V2 to program them, just make sure to follow the datasheet regarding the programming pins (like keeping them dedicated to programming or avoiding low impedance things connected it).

From the ST Link V2 ST website


  The ST-LINK/V2 is an in-circuit debugger and programmer for the STM8 and STM32
  microcontroller families. The single wire interface module (SWIM) and JTAG/serial wire
  debugging (SWD) interfaces are used to communicate with any STM8 or STM32
  microcontroller located on an application board