Arduino Leonardo RX TX mystery
An Arduino Leonardo has native USB support. Which means that it has separate serial interfaces to the PC and to the hardware pins.

Serial is only used for the communication with the PC and is unrelated to the hardware serial pins 0 and 1. Those are exposed trough Serial1.

So, if you are using the exact same Uno sketch, that uses the hardware serial pins, it can't work on a Leonardo, because data is just sent-to/read-from the PC and not to the connected Bluetooth module connected on pins 0 an 1.