This will likely be a multi-post reply as I work on it in chunks, but for starters, I'll try to help define some tool types.
Turning tools all generally fall into three different categories: Gouges, skews, and scrapers. In general, gouges and skews cut the wood with the "knife" edge of the tool, while scrapers actually cut with a very fine burr on the edge of the tool. More on skews and scrapers later. For now, let's look at gouges.
Gouges come in essentially two types: Bowl gouges and spindle gouges. They can both have similar shapes, but there is a difference in how they are made and how they transition and attach to the handle. Bowl gouges are subjected to a lot more stress than spindle gouges, so they tend to be a solid round piece of steel going into the handle. Spindle gouges are typically under less stress, so they forged into shape and transition into a square or rectangular tang (like the end of a file) that's inserted into the handle. Here's an example of a bowl gouge. Notice how it is made from a solid piece of round steel. It has a flute (valley) at the cutting end, but it transitions into a solid round bar going into the handle:
And here is a spindle gouge. It's made from a flat piece of steel that's been forged into a U shape. Notice how the flute ends and becomes a rectangular tang right where it meets the handle:
The wide gouge above is typically called a roughing gouge. It's meant to make the rough cuts to turn a square piece of wood into a round one. A more accurate name would be a "spindle roughing gouge", since it is forged into shape and has a tang. Although you can likely get away with using a gouge like this to do rough cuts on a bowl, it's risky, because there's a decent chance the torque from a bowl-sized piece of wood could snap the gouge off the handle if you got a bad catch. There have been many reports over the years of spindle roughing gouges breaking and flying across the shop when used on a bowl.
To make things even more confusing, some smaller gouges labelled as "spindle" gouges are actually constructed out of a solid round bar like a bowl gouge. These can safely be used in bowl turning, but because of their small diameter, they might not be the most efficient way to do it. (That said, some folks like using small bowl gouges on big bowls.)
Looking at the photos you posted, I'm guessing that your biggest gouge is a spindle roughing gouge because it looks to be forged and appears to have a tang going into the handle:
And this one looks like a typical spindle gouge, again forged into shape with a tang inserted into the handle:
Because of the forged shape and tang connection, I'd caution against using gouges like these on bowls. You can likely get away with it for a while (I did the same when I was starting and learning), but there's a pretty big risk of it becoming an uncontrolled missile flying across the shop if you get a bad catch. (And beginners are more likely to get a catch than someone with more experience in tool presentation and sharpening.)
Bowl gouges range in price from about $25 to over $100. In general, the more they cost the better the steel and the longer they hold their edge between sharpening. Before I started buying really good gouges (
Thompson Lathe Tools, $70 to $120 each without handles), I got a lot of miles out of a bowl gouge like this from Penn State:
Benjamin's Best High Speed Steel 1/2" Bowl Gouge, 22" long. Bowl gouges have a deep flute and are used primarily for turning bowls. Also used for dishes and other hollow forms mounted on the faceplate - normally with the grain running across the turning blank.
www.pennstateind.com
As you shop around for bowl gouges, you'll see the fluted part comes in different shapes (generally U or V shapes) and there's a wide range of tip shapes. If you poke around the Thompson Lathe Tools website, you can see some good examples of the different flute and tip shapes. I prefer a tip shape with the wings (sides) of the tip swept back quite a bit. Other folks prefer a more squared-off tip. The tip shape is something you can change yourself buy how you sharpen it on the grinder. The flute, on the other hand, is not changeable. I have both U shaped and V shaped gouges, and like the both.
More to come later...