Merriam-Webster provides a disambiguation of three words: lie, prevaricate, and equivocate. I will present the definitions and then the disambiguation.
lie (intransitive verb):
1 : to make an untrue statement with intent to deceive <She was lying when she said she didn’t break the vase.> <He lied about his past experience.>
2 : to create a false or misleading impression <Statistics sometimes lie.> <The mirror never lies.>
equivocate (intransitive verb):
1 : to use equivocal language especially with intent to deceive
2 : to avoid committing oneself in what one says
The first (and only applicable) definition of equivocal, linked in the definition above, is:
1 a : subject to two or more interpretations and usually used to mislead or confuse <an equivocal statement>
prevaricate (intransitive verb):
: to deviate from the truth : equivocate
Merriam-Webster disambiguates the terms thusly:
A LIE is the blunt term, imputing dishonesty <lied about where he had been >. PREVARICATE softens the bluntness of LIE by implying quibbling or confusing the issue <during the hearings the witness did his best to prevaricate>. EQUIVOCATE implies using words having more than one sense so as to seem to say one thing but intend another <equivocated endlessly in an attempt to mislead her inquisitors>.
The current Gospel Principles manual (as of 2017-02-06) defines lying and other forms of deception in this paragraph (emphasis added):
Lying is intentionally deceiving others. Bearing false witness is one form of lying. The Lord gave this commandment to the children of Israel: “Thou shalt not bear false witness against thy neighbour” (Exodus 20:16). Jesus also taught this when He was on earth (see Matthew 19:18). There are many other forms of lying. When we speak untruths, we are guilty of lying. We can also intentionally deceive others by a gesture or a look, by silence, or by telling only part of the truth. Whenever we lead people in any way to believe something that is not true, we are not being honest.
So, lying is intentionally deceiving others, and it may be performed in a variety of ways (silence, telling only part of the truth, etc.)
Definition given in General Conference
Marvin J. Ashton defined lying in his 1982 General Conference address:
[His wise schoolteacher had them recite] “A lie is any communication given to another with the intent to deceive.”
When I compare this definition with that found in the dictionary, which states, “A lie is an untrue statement made with the intent of deceiving,” I greatly appreciate her definition. A lie can be effectively communicated without words ever being spoken. Sometimes a nod of the head or silence can deceive. Recommending a questionable business investment, making a false entry in a ledger, devious use of flattery, or failure to divulge all pertinent facts are a few other ways to communicate the lie.
The wikipedia entry for lie (as of 2017-02-06) defines “lie” (emphasis added):
A lie is a statement that the stating party believes to be false and that is made with the intention to deceive.
The article goes on to distinguish between types of lies.
The ones that seem most applicable to Joseph Smith’s words are these:
Big lie: A lie which attempts to trick the victim into believing something major which will likely be contradicted by some information the victim already possesses, or by their common sense. When the lie is of sufficient magnitude it may succeed, due to the victim’s reluctance to believe that an untruth on such a grand scale would indeed be concocted.
Bullshit: Bullshit does not necessarily have to be a complete fabrication. While a lie is related by a speaker who believes what is said is false, bullshit is offered by a speaker who does not care whether what is said is true because the speaker is more concerned with giving the hearer some impression. Thus bullshit may be either true or false, but demonstrates a lack of concern for the truth which is likely to lead to falsehoods.
Contextual lie: One can state part of the truth out of context, knowing that without complete information, it gives a false impression. Likewise, one can actually state accurate facts, yet deceive with them. To say “Yeah, that’s right, I ate all the white chocolate, by myself”, using sarcasm, a form of assertion by ridiculing the fact(s) implying the liar believes it to be preposterous.
Deception: Deception is the act of propagating beliefs in things that are not true, or not the whole truth (as in half-truths] or lying by omission. Deception can involve dissimulation, propaganda, and sleight of hand, as well as distraction, camouflage, or concealment. There is also self-deception, as in bad faith.
Disinformation: Disinformation is intentionally false or misleading information that is spread in a calculated way to deceive target audiences.
Half-truth: A half-truth is a deceptive statement that includes some element of truth. The statement might be partly true, the statement may be totally true but only part of the whole truth, or it may employ some deceptive element, such as improper punctuation, or double meaning, especially if the intent is to deceive, evade, blame or misrepresent the truth.
Misleading and dissembling: A misleading statement is one where there is no outright lie, but still retains the purpose of getting someone to believe in an untruth.
Weasel word: A weasel word is an informal term for words and phrases aimed at creating an impression that a specific and/or meaningful statement has been made, when in fact only a vague or ambiguous claim has been communicated, enabling the specific meaning to be denied if the statement is challenged. A more formal term is equivocation.
Other types of lie which do not seem to apply to any of Joseph Smith’s denials:
Honest lie: An honest lie (or confabulation) can be identified by verbal statements or actions that inaccurately describe history, background, and present situations. There is generally no intent to misinform and the individual is unaware that their information is false. Because of this, it is not technically a lie at all since by definition, there must be an intent to deceive for the statement to be considered a lie.
Lying by omission: Also known as a continuing misrepresentation, a lie by omission occurs when an important fact is left out in order to foster a misconception. Lying by omission includes failures to correct pre-existing misconceptions. For example, when the seller of a car declares it has been serviced regularly but does not tell that a fault was reported at the last service, the seller lies by omission. It can be compared to dissimulation….An omission is when a person tells most of the truth, but leaves out a few key facts that therefore completely change the story.
White lie: White lies are minor lies which could be considered harmless, or even beneficial, in the long term. White lies are also considered to be used for greater good. White lies are often used to shield someone from a hurtful or emotionally damaging truth, especially when not knowing the truth is completely harmless.
Minimisation: Minimization is the opposite of exaggeration. It is a type of deception involving denial coupled with rationalization in situations where complete denial is implausible.