The distinction is worth keeping sharp, and one counter-example shows why all three numbers are needed at once. A highly directive antenna can still be a poor link antenna if its efficiency is low: a narrow beam concentrates what little power is radiated, so the peak intensity can look respectable while most of the input power is lost as heat or trapped in nearby structures. Directivity alone therefore says nothing about how much power actually leaves the antenna.
The reverse case is equally common. A small antenna with modest directivity can still deliver useful gain if its efficiency is high and it is well matched, because gain already folds efficiency into directivity. That is why comparing a high-directivity array with a low-directivity element on gain alone can mislead: the array may win on peak direction but lose the link if its feed network is lossy or its beam points slightly off target.
Realized gain is the number that matters for a link budget, because it also includes mismatch at the feed. An antenna can show good gain in a simulation with a perfect port and then lose a decibel or more once the real feed, connector, and nearby ground are included. When a datasheet quotes gain without stating whether mismatch is included, I treat it as incomplete and ask for return loss at the same frequency.
Two measurement traps complete the picture. First, total efficiency and radiation efficiency are not interchangeable: total efficiency includes mismatch, radiation efficiency does not, and mixing them makes gain calculations inconsistent. Second, the reference matters. A figure quoted against a dipole rather than an isotropic radiator differs by about 2.15 dB, which is enough to reverse a close comparison. Stating directivity, efficiency, realized gain, frequency, and reference together removes most of the confusion these three terms usually cause.
