Good for you for noticing these differences. Sensory science is a long way from describing, let alone explaining these distinctions. Until they do, here's my point of view.

It is generally held that astringeny or harshness is caused by the binding of long-chain polymerized tannins to salivary protein. The slick coating of the mouth is stripped away and replaced by a grainy precipitate resembling sandpaper. We can even use sandpaaper grit sizes to grade the fineness of the astringent impression. The longer the polymeric chain, the coarser and drier the impression.

Young red wine has a grainy sort of tannin on the tip of the tongue which the French call "green tannin" though it doesn't mean underripe or vegetal. I believe this tannin is caused by coextraction colloids -- tiny beads of unpolymerized phenolic monomers, half color (anthocyanins) and half tannin precursors. Since this form isn't stable, you rarely see this type of tannin in a bottle.

Why is there astringency if there's no polymerization? Leading oenologiste Michel Moutounnet of Montpelier suggested to me that the salivary protein is binding with the surface of the beads, so you get coarse tannin even though it's all monomers.

Phenols can form daisy chains either oxidatively or non-oxidatively. The latter leads to long, dry, grainy, dirty tannins, particularly in wines of low color or prolonged hangtime. We call this "dry" tannin, and it's the only kind that gets under the tongue in the back of the mouth, besides trashing the palate generally. This happens when we try to make red wine as if it were riesling, depriving it of oxygen through use of stainless steel and inert gas.

Barrels, racking, and other forms of oxygenation help red wine breathe, and quickly convert green tannin instead to a sheet-like grippy tannin atop the palate that resembles peanut butter in that it makes the tongue stick to the roof of the mouth. This "hard" type of astringency, though unpleasant, is a good sign that the wine can age well, whereas dry tannin (grainy, under the tongue) is a sign the wine is dying.

After sufficient oxidative development, hard tannin looosens its grip and begins to "melt" from the back of the mouth, progressing forward over time. This "plush," "velvety," or "soft" tannin is quite stable and has properties of aromatic integration which incorporates the aromas of wood, vegetal notes and Brettanomyces aromas into a less obtrusive background so the wine speaks with a single, soulful voice.

Lastly we have oak tannin, which occurs in the front of the tongue but not on the tip. It is very fine but also very drying, and contains anaesthetic compounds such as eugenol (used to numb gums in dentistry). We call this "parching / numbing" tannin. With today's rampant and artless use of staves and tannin additives, we often see this aspect in bottled wines. It's easy to spot by the hollowness in the middle of the tongue. Oxygenation can convert this tannin to an impression of fatness if skillfully applied.

The most important contributor to good tannin structure and finesse is to have lots of unpolymerized anthocyanin pigment present. These color molecules can't "daisy-chain" or polymerize -- they're the "bookends" on the polymer, so the average chain length is shorter if you have good color. That's why syrahs are softer than pinot noirs despite much higher tannin levels.