Hi........ I've got the time to tackle a part of one of these terms for you right now before I get back out to the studio. As a woodfirer since 1969..... I'll tackle one that is kinda' directly wood-fire related.
Warning....... a bit technical

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緋色 hi-iro (fire stains)
"Hi" is "fire" in Japanese and "iro" is color. So the literal of that term is "fire color". Hi-iro is a sub-category of a whole plethora of "youhen" effects on the clay and glazes. "Youhen" translates a "changed by the fire" or "fire change".
Hi-iro effects on "yakishime" pieces are often refered to by American (and most western) potters as "flashing". "Yakishime" pieces are works that go into the kiln unglazed and are totally surface-embellished by the actions of the firing. Traditionally these effects are produced in solid-fuel burning kilns. Usually wood fired.
Hi-iro effects on glazed wares usually involve the changing of the glaze coloration where flame and ash impinge on the covering of glaze, causing the surface qualities or color to change from the overall "normal" background glaze color. I'll leave that answer for another time (or person).
Wood is more than just a source of heat in a kiln. The contents of wood ash contain chemistry that, when combined with the silica ( SiO
2 ) contained in a clay body, can cause the formation of varying types of partially to fully melting glass deposits on the surface of the clay. The exact state and nature of this melt is classified into a large number of distinct effects by Japanese tea masters, potters, and museum curators.
The subtleties of these distinct definitions are great. Worse, sometimes potters in different regions call the effects different "names". Sometimes the same names are used for different things in differnt regions. It CAN get a bit confusing sometimes

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"How many angels can dance on the head of a pin?"
The prime constituent of wood ash is calcium oxide ( CaO ). At high temperatures (1000 C and up), CaO is a very powerful flux (melter) which brings the melting point of pure silica ( around 1800C) down. Deposits of wood ash on the surface of unglazed clay are the basis for the effect called "shizenyu" or "natural ash deposit glaze".
Clay bodies used by potters would not stand up to the firing temperature of pure silica .....so the art and science of developing glazes has required the use of fluxes to make glazes possible. In fact it was the observation of the melting action of wood ash on the surface of clays in wood kilns that helped spur the actual act of applied glazing in high fire ceramics (for example, see the historical "Sanage" work in Japan).
Also present in wood ashes are somewhat heavy concentrations of sodium compounds ( sourcing Na
2O ) and potassuim compounds ( sourcing K
2O ). Soduim oxide and potassium oxide are also VERY powerful fluxes on silica. They are both active on silica starting at much lower temperatures than CaO is. So they can become very active ion the firing process that goes to high temperatures.
These Na and K bearing compounds are volatile at the temperatures found in the fireboxes of wood kilns. You could kind of think of the idea that they turn into Na and K "steam". So during the firing, the sodium and potassuim form some "fumes" that circulate in the kiln following the path of the movement of the flames. They "find" the silica on the surface of the clay they come in contact with, and form thin layers of sodium rich or potassuim rich (or both in reality) glass.
In areas that also have the physical wood ash being picked up by the kiln's draft, the Na
2O and K
2O compounds join in with the CaO and form an overall glass that is fluxed by
all of them. One of the mechanisms of this is that because the K
2O and Na
2O glasses start to melt at a lower temperature than the solely CaO based compounds, the deposit of the K and NA based glass starts to become "sticky" like flypaper earlier in the firing, and "grabs" more wood ash floating by.
Sodium and potassium fluxed glass (without the presence of significant CaO) has a specific chemical characteristic that it tends to render any iron oxide present toward the red state ( Fe
2O
3 ). This is a very different color rendition from a predominantly CaO fluxed glass, which tends to "bleach" iron oxide into disappearing, or tends toward a greenish or brownish coloration. All stoneware clays and even most porcealins have iron oxide present in them. Stonewares have
much more iron than porcelain. Clays from different sources have more or less iron content; for example the usual clay used in Bizen is very high in iron, whereas the usual clay in Mashiko has much less iron.
So in locations in the kiln where the soduium and potassuim circulate onto the surfaces of the ware AND in the places that the physical ash deposits with their high CaO do NOT also tend to land....... the thin layers of K
2O and Na
2O glass form areas of reddish "flashing" on the raw clay surface. The flashing character is influenced by the way the piece's form disrupts the flow of gases over that form. This creates the wonderfully "naturalistic" patterns on the shape of the piece.
These markings are designated as one category of "hi-iro" on yakishime wares.
There are some more mechanics that are also within the pervue of the term "hi-iro", such as when some carbon compounds get trapped into that low melting K
2O and Na
2O based glass..... possibly producing some greyish, bluish, or blackened effects. When/if I get some time....... more on that one later.
Hope this is a start to understanding more about pottery, and Japanese specific terms. I am sure that others will chime in here too.
best,
................john