The word threat is used for a sente but there is no consensus about the meaning. The following meanings are possible or have been used:

1) the initial move or sequence that is sente and should be answered

2) the executing move or sequence after the initial move or sequence that is sente, if the opponent ignores

3) the position after the initial move or sequence that is sente

4) the combinatorial game after the initial move or sequence that is sente

5) the count of the position after the initial move or sequence that is sente

6) the move value at the position after the initial move or sequence that is sente

7) the move value of preventing the sente by playing reverse sente

Quite like for 'ko threat' and its, let me call it, 'execution', I like to speak of (1) as the 'sente threat' and (2) as its 'sente execution' but others have used the word 'threat' in one of the other meanings. More often, 'threat' of a sente has been used carelessly as if it were a term but without clarifying the intended meaning. Therefore an alternative is to avoid speaking of (sente) threat at all.

Is there a meaning that should be preferred and, if so, WHY?

The Japanese term
劫立 (kōdate)
might derive from
劫を立てる(kō o tateru)
which might have a meaning similar to "make the ko stand".

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The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)

Consider the statement, "Get out or I will call the police." That statement is a threat, and it carries a threat, the threat to call the police. Metaphorically, we apply the word, threat, to go in both senses.

In one sense, any play with a follow-up may be said to carry the threat of that follow-up. Usually we do not apply the term to the follow-up of a gote, reserving the term for the follow-up of a sente. In fact, we may define one meaning of sente as a play that makes a threat that should be answered. In your list of suggested meanings you make reference to the values of plays or positions. These are considerations that may apply to whether a threat should be answered, but not to whether a play is a threat or carries a threat.

In the other sense, a play which carries a threat may itself be called a threat. Typically, we restrict that meaning to ko threats.

Edit: In the case of ko threats, we may say that a play is not a ko threat if it does not carry an effective threat, so that if it is ignored, that threat is not played.

Also, in the West, the term, ko threat, has been extended so as to be almost meaningless, so that any play is a ko threat.

And, under hypothetical play in Japanese rules, a pass may be considered a ko threat in the sense that it carries the threat to take a ko.

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No, because 劫 here is being used in its meaning of 'ko threat'. Tateru is used idiomatically for a wide range of things that ultimately mean making or establishing (e.g. making plans, making tea). It may be just as loosely related to the underlying meaning of 'stand' as 'stand' is in 'understand'.

The usual way to talk in Japanese about a move we call a ko threat is to say it is a move seeking compensation. But, having said that, let us not forget that the basic meaning of 劫 itself is 'threat' (nothing to do with aeons - that's a fairy story). The commonest word for 'threaten' that appears in Japanese texts is probably obiyakasu, which is rarely or never used in connection with kos. It usually appears as 脅かす, but it can be written 劫かす. Obviously that usage is avoided in go books.

Thank you very much indeed for the correction.
And the insight into the Japanese language.

I suppose that there was some wishful thinking involved when interpreting Japanese with a Japanese-English dictionary only.

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The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)

Have you ever thought about the possibility that "threat" has nothing to do with "sente" ?

@ 1)
If a move "SHOULD" be answered (i.e. answering is the absolute best play) then this move cannot be a "threat"; it is an "absolute attack", for example.
The "real threat" is "Answer or I will win!".

On the contrary, giving atari at two opponent's stones carries a threat (of capturing these stones), and (as Bill pointed out) usually is also called a "threat". But it might depend on the situation whether this atari will be "sente" or not.

@ 2)
You will be able to realise the "threat" that is carried in your move, only if your move has been "gote".

Do you remember the saying "Sente gains nothing" ?

_________________
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)

My understanding is: Your move is a ko threat if you hope that your opponent will not answer it.

I don't know about Japanese, but in Chinese ko threats are called "ko material", as in "stuff used for kos". It's not the same idea as a threat at all.

I refer to 1) as the sente, 2) as the threat of the sente. Sometimes I slur 2) to refer to 3). I don't know what 4 is, I wouldn't use "threat" to refer to 5), 6), or 7).