When should I use USART instead of UART?
For your purposes, the UART and USART are the same thing.  UART stands for universal asynchronous receiver/transmitter.  The additional S in USART stands for synchronous.  It's just a little added capability Microchip gave the module to make it more useful in some cases.  That extra capability doesn't apply in your case.

The PC COM port only takes a UART to talk to.  The fact that the USART could have been used in a different way is irrelevant to you, except that maybe you have some additional configuration bits that have to be set the right way.