Truth and honesty amount to different concepts: from about the 14th century—when, as it happens, many words in English started to shift their meanings—“truth” came to refer to “that which is correct” or “accuracy”; however, in its Old Germanic roots, the word suggested “faith, faithfulness, fidelity, and loyalty”—as in, “old friends, good and true”. As with all these genealogical investigations, this does not negate the current usage; although, clearly, we somewhat carry on the old meaning with the word—it might be a bit archaic, but you could still just about say someone was “true to their word.”
Truthfulness is, therefore, tied up with faith and priesthoods; it is the priests who have the truth—possibly truths—in which they have confidence and faith; they are loyal to these views even unto death. Christ was said to be the Logos; a difficult concept, but one that certainly included “truth”—you could have faith and confidence in Christ, although whether Christ’s truth was the same thing as what we mean by “that which is correct” is another matter. Nevertheless, priests definitely want you to have faith and confidence; they are very interested in “truth”, in its earlier sense—and it could be said they are now in conflict with a new priesthood, scientists, who speak about truth in regards to “that which is the case” and “accuracy”; if both these conditions are fulfilled you can have confidence in the results from the scientific method—it is the truth.
“Honesty”, by contrast, originates from “honour”—“glory, renown, and fame”; it is connected to virtue, to masculinity—to effective action that leads to glory, perhaps even beauty. It is a subtractive concept—being “free from fraud”—whereas “truth” is a positive concept. Via negativa: remove fraud, remove error—do not add anything positive. Rather than a promise to deliver accurate or correct results, honesty promises to remove errors. In its association with glory, renown, and virtue honesty is a warrior or aristocratic concept; and this is why Nietzsche advocated for it, he thought that people had come to hide behind “the truth”—in which they professed great faith and confidence—even though the truth, their security blanket, was supported by many lies; time to become more honourable, more warrior-like, and remove the fraud: let us have effective action, glory, and beauty—let us have more honour-sty.
Also in the 14th century, “honesty” became conflated with truth—an honest individual was truthful. However, if we look at the etymology, this is not quite the case. A priest may have his beliefs—a term also related to truth in its earlier sense—in which they have confidence or faith, yet honesty might strip away the lies that support that truth; and this is what Nietzsche partly set out to do in his work as destructor: enough with the warm blanket that covers up so much, the truth—time for bracing honesty, some frank soldierly talk and not the truth that reassures women and children.
Truth is a spiritual concept in the deepest sense, for its etymology goes back to -deru; it goes back to wood, and wood is symbolically spiritual—the same root gives us druid. You knock your knuckle on the wood and it “rings true”; in this sense, truth is not dissimilar to Nietzsche’s idea that you must “philosophise with a hammer”—a tuning hammer—to find out what “rings true”; yet this is not quite the same as accuracy or being correct.
Truth is quite a slippery concept, in the sense that it is a concept we must have faith or confidence in. People may be quite prepared to lie to preserve a truth; although, probably, this will not be sustainable in the long-term—although it might be quite some time before reality presents its bill. Honesty is more bracing, cold, and sceptical: it offers integrity; its only consolation is that you have not been deceived—although it offers nothing to positively have faith in.