USB Host and Device communication happen in the same controller preferably Pic controller
You can achieve that with some PIC32 devices which have 2 USB ports.
The Microchip Harmony stack, however, is not properly tested/working (despite what advertized) when working with both ports at the same time in host/device configuration.
You may need to implement your own USB stack or use some that are available online.
In my case, I used Harmony stack for the USB Host side and a stack found online for the USB Device side.
The port type is only related to what USB connector you choose.