But the point is to have a word that points to the thing that is in common between those two cases: the action of professing a belief
because it is good PR, whether or not it is true. It is the single-act equivalent of what would be referred to as "sociopathic narcissism" if it was a continuous property of a person: a desire to look good that will use the truth if the truth suits, or a lie if a lie suits, without caring which is which.
To be clear, usages of the term "virtue signalling" to describe the behaviour of an individual, don't usually usually imply the same degree of sociopathy that it does when applied to the actions of a corporation. An individual doing "virtue signalling" is simply learning signals that tend to make people react by calling them a good person, and then parroting those signals, without necessarily doing much to learn about the content of those signals.
A better term for the individual behaviour might be "cargo-cult virtuousness"—which makes even more sense when put together with an assumption that people will be cargo-culting the "ritual" of a virtuous behaviour from other people who also cargo-culted the ritual, and so the ritual being performed will decay in this retransmission until it consists only of the observable actions that get people to call you virtuous, without holding any of the content that actually is virtuous.
Which is to say, in an environment with centralized teachings of moral ritual (like a religious congregation with active preaching), the only kind of virtue signalling that works is to actually do consensus-virtuous acts, because everyone is both aware of what the virtuous rituals are, and also aware that everyone else is aware of what the virtuous rituals are. In such an environment, it requires an active intent toward deception to merely signal virtue.
Meanwhile, in an environment where the idea of virtuous ritual is merely spread memetically, between families and peer groups, it is easy for a the idea of a virtuous ritual to become corrupted such that people can actually think themselves virtuous (and others can actually think that person virtuous) based solely on the performance of the "hollowed out" virtue ritual.
To reiterate, the point of virtue-signalling is to point to the thing that goes on in both contexts above: the thing that is active deception in communities with centrally-dictated virtue ritual; and the thing that is unquestioned cargo-cult-ism in communities with peerwise-transmitted virtue ritual.