What are different ways of remote communication two circuits?
As mentioned in the comments, UART and I2C can be considered to be physical hardware connections with a defined method of signaling. I2C is a hardware bus generally used for communication between chips (often on the same board), and involves a specific timing and signaling method. UART also has it's own timing, but is a more universal way to transmit general serial data between just two devices.

Bluetooth is a wireless communication protocol. It defines how two devices handshake, communicate, transmit data, check in, etc. with each other. However, since Bluetooth uses UART to move data around on the hardware side, you can almost think of a Bluetooth link as a virtual UART connection between two devices, but with a lot more complexity and functionality underneath. Using Bluetooth wouldn't really be as simple as issung a "uart.write()" command, for instance.

I think you should look into using something like the XBee. An XBee literally is a virtual link between two UARTs and would keep your wireless communication as simple as possible.

All you'd have to do is hook up an XBee to the transmitter's UART (PIC24 side), and hook up an XBee to the receiver's UART (is this also a PIC24?). Once you do that, you can do a simple UART read/write on either side and it would be as if you had wires connecting the Tx and Rx pins.