I'm not sure if this is the “official definition” if there is such a thing, but I have the inscription “deep ping” used with respect to functionality that allows (unlike regular ping) to send a message to a server that goes through as much as possible web stack before returning the answer "ok".
As an example, you can make a ping transaction that goes from the network right down the stack to the database and makes a dummy choice to read ok from the dummy table and return this result. This allows (in contrast to the "normal ping", which only checks the network), the confidence that all layers in the application, including the database, are really alive.
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