US : jam/jelly/preserves/etc
In the US, there are specific definitions from the Food & Drug Administration on what can be labeled as jam, jelly, etc.
From CookingLight.com, but preserved here in case of link rot:
Jelly is a clear, bright product. It is generally made by cooking fruit juice and sugar with pectin as a jelling agent and lemon juice as an acid to maintain a consistent texture. Jelly is firm and will hold its shape (it 'shakes'). Generally, jelly contains no pieces of fruit, although specialty jellies, like pepper jelly, may include pieces of jalapeño or other pepper.
Jam is made from crushed or chopped fruit cooked with sugar, and often pectin and lemon juice. Jam can be a purée of fruit or have a soft pulp, but it does not contain chunks of fruit.
Preserves are fruit cooked with sugar to the point where large chunks of fruit or whole fruit, such as berries, are suspended in a syrup base. The texture of preserves is not smooth like jelly or jam.
Marmalade is a soft jelly, often citrus-based, that includes both the flesh and peel of the fruit suspended throughout the jelly base. The bitterness of the peel offsets the sweetness of the jelly.
Conserve is a mixture of more than one fruit, often with added nuts and raisins, that is cooked until it becomes thick. It is used as a spread for breads, pastries and meats, and in the latter use is closest to chutney.
Chutney is a spiced condiment of Indian origin (chatni is the Hindi word for strongly spiced) made of fruit or vegetables. It is typically served as an accompaniment to food, not as a spread. The spice level can range from mild to hot, and the consistency from a fine relish to a preserve or conserve. Fruit chutney consists of chopped fruit, vinegar, spices and sugar cooked into a chunky sweet-tart-spicy mix: according to one explanation, it 'blurs the Western distinction between preserves and pickles.'
Fruit Butter, such as apple butter or prune butter, is fruit purée or pulp combined with sugar, lemon juice and spices, slowly cooked down to a smooth consistency. The 'butter' refers to its spreadability: there is no actual butter in the product.
Fruit Curd is a creamy spread made with sugar, eggs and butter, generally flavored with citrus juice and zest.
Fruit Spread is generally a reduced-calorie product made with fruit juice concentrate and low-calorie sweeteners replacing all or part of the sugar.
In my book, this is pretty trivial. Wasabi is absolutely a spice - it's something with a very specific flavor, derived from a plant, that can be used in fairly small quantities to add flavor to something.
It's not spicy (spicy hot, piquant) in the normal sense, though. It doesn't contain capsaicin. It is hot in some sense: it contains allyl isothiocyanate, which we obviously have a very strong reaction to. This is the same compound that's in horseradish and hot mustard. The reaction is very different from capsaicin, though. Capsaicin causes you to register heat at a much lower temperature than you normally would, so you're actually feeling heat, like you would if you were burning your tongue. It's quite literally hot, as far as your body is concerned. It's also an oil, so it can't be washed away easily with liquid, and the burning tends to linger. Wasabi, on the other hand, doesn't produce an actual sensation of heat, you feel it mostly in your nasal passages, and can easily be washed away with liquid, so it tends to be a brief sensation. So sure, "hot" is a reasonable way to describe it, mostly because we don't have a word for the actual sensation, but it's definitely not the same thing as a hot pepper.
I'm sure you can find plenty of people who would say that these are just two different kinds of spicy hot (piquancy), but arguing over definitions isn't going to get us anywhere. The important thing is that there's a fundamental difference, and there's no way you could substitute one for the other. If you want to understand why I think this (and it's not just a personal definition), go to any recipe site, search for "spicy", and see how many things with wasabi/horseradish/mustard supplying "spiciness" you find.
Edit: To stave off further debate in the comments, let me just repeat: arguing over definitions is not useful. There are probably a lot of people who think "spicy hot" should include this, and a lot who don't. I wouldn't generally expect anyone to think of wasabi without context when you say spicy hot, but you're welcome to use the terms however you and the people you talk with understand them.
Best Answer
You do.
There is no official list of delicacies. No authority on deciding what food is tasty. If, to you, lavender chocolate is a delicacy, then you can say so. Others will say that it isn't, that it tastes like soap and, and they can't bring themselves to eat it. Saying "I like bacon" is just a personal statement about your preferences. Saying "Bacon is a delicacy" is a personal statement which carries a bit more information, namely that you find bacon tasty, but also consider it a luxury food item, as opposed to an everyday food (although this second semantic distinction is somewhat lost nowadays).
As tastes tend to be shared within a culture, you will probably find that the people around you tend to agree somewhat on what is a delicacy, although it's not a complete overlap. This can appear as if there a universal agreement on what is a delicacy. And I don't doubt that somebody, somewhere has compiled something they call a list of delicacies, the same way that a movie fan will compile a list of "really funny comedies". Both have equally little validity - what is funny to that person will not always be funny to you, even though there will be a correlation if you grew up in the same culture.