Why A link budget is an accounting of all the gains and losses in a communication path, starting with transmitter output power, adding transmit and receive antenna gains, and subtracting feedline loss, path loss, and other system losses. The result is the signal power arriving at the receiver input, which you then compare to the receiver's sensitivity or noise floor. The amount by which the received signal exceeds the minimum usable level is the link margin.
Watch out The choice listing only antenna gains minus losses leaves out transmit power, which is the starting point of the whole calculation; the choice about transmit power minus receiver sensitivity skips the path and system losses entirely and describes something closer to a crude margin estimate.
Budget = power in, plus gains, minus losses, measured at the receiver. What's left over is your link margin.