Tensioned blades are so called because they are forged so thin that using them would cause the blade to collapse. Tensioning is a kind of peening done during the manufacturing process after heat treatment (hardening and tempering) where the blade is dimpled all along its surface with a mechanical hammer. Each of these blows spreads the metal a little, creating tension much like stretching the head of a drum. This imparts rigidity that would otherwise be lacking in a blade so light and thin. However, both because of this process and because of the desire by their markets to use peening as a method of bevel maintenance, the blades must be soft so they remain ductile. Most Continental tensioned blades are only about 45 on the Rockwell C hardness scale, which is about the same as a "Made in Mexico/China/India" hardware store axe--quite soft indeed. However, in this state, it's quite ductile and responds well to both tensioning and edge peening without being prone to high rates of failure from cracking as would occur with harder steel that thin. However, when heat treated to that low of a hardness, the edge is also not very wear resistant (because of the crystal phase the steel is in: a phase known as pearlite) nor is it very resistant to deforming. As a result if you were to simply file an edge on a Continental blade you'd have an edge that both blunted and rolled very easily. That's where peening comes in. Mechanical deformation of the metal when worked cold disrupts the crystal lattice structure of the steel--that is to say, the neat and orderly crystal structure gets pushed around and distorted. The more this is done, the more resistant to further deformation the steel becomes, and the more prone to cracking it becomes. This is why when you bend a paperclip back and forth repeatedly it eventually breaks: the crystal lattice has been so deformed and torn that it cannot continue to bend, and so cracks instead. This is known as "work hardening". Now, when you peen an edge, it doesn't increase wear resistance, but it does help make the edge less likely to blunt from rolling over--that is to say that it improves "edge stability." But one must be careful not to over-peen the blade to the point of inducing cracks, because the tension of the blade is just looking for an excuse to let go, much like flipping an orange peel inside out and then snipping one edge of it. The tension wants to release by spreading apart cracks whenever it's able, and so if you were to induce a crack in peening and then accidentally snag the toe of your blade on something nasty hidden in the grass you could end up putting a very deep tear in the blade, and I've often seen such damage in heavily-used vintage blades. Thin blades not only make the blade light, but make peening faster because you are working a section of steel that is essentially pre-thinned for you.
Un-tensioned blades achieve their rigidity by thickening the blade (rigidity increases cubically with thickness, so a little extra thickness adds a lot of rigidity), heat treating blades harder, and in the case of American and English blades, using a stiffening "rib" in the form of a V-like channel along the spine of the blade rather than a simple upturned chine. To keep weight down with this increase in thickness, the blades are made narrower, though often with a widening at the heel of the blade so that the web (the flat span of thin steel between the edge and rib) is deep enough to cut thick-stemmed weeds without bottoming out. Many American, English, and Nordic blades were laminated to allow the blades to have glassy-hard edges while remaining tough and shock-resistant. A layer of high-carbon edge steel would be forge-welded between strips of soft cladding iron that provided support and toughness. More premium versions even had a strip of medium-carbon spring steel laid into the "sandwich" behind the edge steel so the spine would have a springy temper to it. "Whole steel" blades that weren't laminated had to make a decision to veer more towards toughness or edge retention, because without the lamination they couldn't equal laminated blades in both categories at once. Most shifted more towards the side of toughness, though some (notably those by Kelly) decided to make their blades extremely hard even though they were whole steel. Even tough whole steel blades tended to be around 52-55 RC (Rockwell C hardness) while very hard examples could get up around 58-60. For reference, a genuine Victorinox Swiss Army knife has a hardness of about 55-56 RC and good quality machetes are usually 52-54 RC. By heat treating the blades harder, the steel has a higher percentage of a crystal phase known as martensite, which is both more wear resistant and more readily supports a fine edge apex. As such, the edge is able to be more readily brought finer and then holds that edge longer. I personally observe something roughly between 3-5 to 1 difference in edge holding vs my Continental blades (even including my Russian ones) and I'm more easily able to bring the edge to very high sharpness. There are several reasons why you don't want to peen these blades, one being that their hardness makes them much more prone to cracking if hammered on as much as is required to shape the bevel in their thicker steel, and the other is that since many blades were laminated, peening a laminated blade would result in your edge being made of the iron instead of the steel, like so:
Instead, these blades are ground equally on both sides, or if the angles on each side vary, they at least reach their apex in the center of the blade where the edge steel is. As a general rule it's best to treat all of your American blades as if they are laminated because it instills good habits of maintenance when working from blade to blade. Ideally this is done on a water-cooled large diameter grinding wheel, but an inexpensive and effective alternative is to use a proper grade of mounted stone grinding point in a drill. I don't have them on hand at the moment, but I've been able to track down a good source for specially formulated ones made for use on thin sections of hardened heat-sensitive steel, and for only about $15 they work pretty great. A hand file can also be used as long as your blade isn't a crazy-hard one and the file is fresh and good quality. Because of the much slower wear you don't have to whet the blade so often and so usually only have to grind the bevel 1-3 times per season, so long as you don't damage the edge to the point where a hand whetstone can't iron it out.
In American terminology blades primarily came in bush blades (for volume mowing of green woody targets up to about thumb thickness), weed blades (for volume removal of heavy weeds ranging through medium-volume lush vegetation removal) and grass blades (for volume removal of lush vegetation, perhaps with interspersed or semi- to infrequent weeds) but there were pattern variations within those categories that made certain blades and lengths better suited to certain kinds of growth and terrain. For grain harvesting, grain cradles were used, and the blades averaged 48" in length with a broad web to help hold the cut stalks on the cradle.
In modern English-speaking Continental style terminology blades are usually referred to as bush, ditch, and grass blades, with ditch blades being the equivalent of a weed blade, just by a different name.
Blade length is mostly determined by the difficulty of the mowing. Since there is only so much force the body can sustainably generate in a stroke for endurance use, that force has to be applied to a given area along the arc of the stroke. The easier the mowing, the longer the blade can be/the more open you may hang it, allowing you to take a deeper and/or wider swath, while more difficult mowing means you need that force to be more concentrated, so a shorter blade keeps you from over-extending yourself and reduces the size of your swath.
Different geographical regions preferred different amounts of curvature at different parts of the blade, different tang angles to match their regional snaths (by the way, American and most English blades came from the factory with the tang flat and the user would have the tang angle adjusted by a
local metalworker or do it themselves, for a custom fit) and preferred different weights, widths, etc. in accordance with their local vegetation, terrain, mowing tasks, and the like, as well as just plain old personal preferences.