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OK, thanks for the hint, I lookd up that word difference now. (What I understand now is that tie implies equal score (a jigo), while draw implies “ending without either side winning”.)
However, I understand long cycles to be seen as not ending the game in e. g. japanese rules. It's just that it's accepted that the game will never end, and never have a result, and so the players just do something else. Of course, the difference to a “real” draw might be purely philosophical.
For all practical purposes, you have enough grasp of the terms, but if you are seeking precision, you need to take account of cultural as well as semantic differences and associations.
Most English speakers are coming to the term 'draw' from chess and soccer. In chess a draw was originally just a game that never ended (e.g. from lack of mating material) and, to get a decisive result, the game was just replayed. But as tournament go developed, it was the British Chess Association that introduced the concept of giving a half point each. That idea proved popular. The association of a draw with a half point each thus became strong and was reinforced by using the same idea in soccer and other field sports in Britain and Europe. Originally, a win was scored 2 points for the winner and 0 for the loser, but a draw was counted as 1 point each. In recent years that has been amended so that the winner gets 3 points, but a draw still gives equal points. This idea of draw = equality is still very dominant, but is not entirely fixed in chess. There have been experiments with giving both sides different point scores depending on whether they were lack or White. And of course the idea of avoiding draws by using penalty shoot-outs has become ubiquitous in soccer. But, still, in chess and cricket, draw = equal points is still an idea that comes readily to British and European people.
It's quite different in cricket, but that excludes Europe, and so usage there is limited to Britain and the worldwide Commonwealth. There, a draw is almost entirely seen as a game that hasn't finished properly (there are players still to bat - the game is ended by bad weather or lack of time). Until the advent of one-day cricket in recent years, it was vanishingly rare for a cricket game to end with equal scores. It is still not common, but now when it occurs there is a strong tendency to call that a 'tie' as opposed to a 'draw'.
In the USA it's different. As I understand it, in field sports there, they always call a game that finishes in normal play with equal points a 'tie'. As I mentioned, that term is easily understood in British/worldwide English. But is not often used. and if it is (e.g. in cricket), we still think in terms of acceptable equality. But a tie in the USA is seen as
unacceptable equality. In baseball, for example, extra innings are played until a decisive result emerges. In American NFL football (and basketball?), I believe, that overtime (the British term is extra time) is used to a decisive result, though a tie is still possible when that time expires. Even then, though, the pressure from fans or the media is such that a team is expected to make a risky play to avoid a tie. The concept of honourable draws (as in e.g. boxing) doesn't seem to fit well with the American psyche.
In Japanese baseball, the concept of extra innings also applies but with the major difference that there is a limit of three each (games are time limited for neighbourhood noise control, etc), and if the result is 'equal runs' after that, that is what it is called (同点). Or other terms such as 均衡 (equilibrium) are used. 'Tie' タイ as borrowed from English is sometimes used (and is used for e.g. a tie in music) but tends to be avoided. I imagine that's because another word pronounced 'tai' 対 meaning 'versus' is so common in baseball that it would cause confusion.
Anyway, the upshot is that Japanese people are not conditioned to use the English term 'tie' in go, and in any case go long precedes baseball. So they use a native solution.
Two terms exist, both with very different connotations.
A 'jigo' is when a game is finished and the players have equal points (with or without komi). But that does not automatically mean it is counted as a half point each in a tournament reckoning. In old go, a contest was a series a games between two players, and if the overall score difference became big enough, the handicap was adjusted. Jigos in that case were essentially just ignored. Later, when tournaments evolved, the dominant type was the win-and-continue. When a jigo occurred in that case, the game was replayed. However, sponsors got wise to the fact that some players were contriving jigos just to get an extra game and thus an extra game fee. That led to a change in tournament structure - either pyramidical knockouts or leagues. In a knockout, a jigo would still have to be replayed, but in a league it could be counted as a haf-point each. However, that was not a given. In the original Meijin league, a jigo was counted as a win for White, but as inferior to a non-jigo win. This rule famously cost Go Seigen his chance to become the first modern Meijin. In short, unlike draw in English, jigo does not have strong connotations of a 'half-point each'.
The other relevant term in Japanese is mushobu 無勝負. This literally means 'without win or loss' and is reserved for those cases (including triple kos) where a game does not finish in a normal count-uppable manner and so does not have a decisive result. There are no special connotations here - it is just taken literally.
Korea and China have largely followed Japan as regards pro go, and so their terms overlap to a fair degree, but there are some practical differences. For example, the Chinese did formally take the step of defining superkos and incorporating them in their rule book. But in practice no-one has taken a blind bit of notice of that rule and so triple kos and the like are treated like mushobu. The anti-superko reasoning seems to be a combination of various factors: they are relatively rare; most people don't like mathematicians interfering in the game; it's seen as too awkward to implement; there's a desire to stay in step with international partners and avoid disputes (some Oriental sponsors have operations in all or some CJK countries).
In English, the term 'void game' has become common for mushobu (and that is the one used in the GoGoD database). It is a very explicit and therefore useful term, free of too many (or the wrong) connotations. Jigo appears to be the favoured term over 'draw' or 'tie', and as far as I can make out has similar, if diluted, connotations to the Japanese usage, which also seems useful.
PS One possible idea to avoid replaying drawn games in go might be to follow the penalty shoot-out idea and to make the players do a series of tsumego problems. Or one, and the first to solve it wins.
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Note: just in case I did not understand what was going on, I also checked the announcement of Otake reaching 1,300 wins last year. There also the reported winning percentage matched the calculation = wins / (wins + losses), excluding his 5 jigo and 1 mushoubu.