For Vision, Daylight and Bright Are The Same

For vision and hiding purposes, there are only three levels of light, as you mentioned. Bright, Shadowy, and Darkness.

"Bright" in this case means it's bright enough that there is no hindrance to vision at all. "Shadowy" grants concealment, and Darkness creates effective blindness if you can't mitigate it.

So yes, for these rules, a torch you're holding and the sun are the same thing, within the "bright light" range of the torch (20'). Outside of that range, the torch stops providing bright light. Get some distance on someone with a torch and you move into shadowy illumination against them instead. (If you have different vision modes than they do, you could actually have different conditions to see them then they have to see you, depending on the light.)

example:

If you're holding the torch, you're in bright light and can't Hide without Cover.

If someone else is holding the torch and you're 5' away from them, you're in bright light and can't Hide without Cover.

If someone else is holding the torch and you're 25' away from them, you're in shadowy illumination. That grants you Concealment, and you can Hide.

The same rules apply for any light source, you can use the Vision and Light table for the effective ranges of different light sources.

So what's Sunlight do?

The sun creates both bright light and bright sunlight. The difference is only in the case of monsters or effects that mention something related to that, like an Orc:

Orcs are dazzled in bright sunlight or within the radius of a daylight spell.

A torch doesn't generate bright sunlight, so in this case it's different.

This Creates Lots of DM Interpretation

As you noticed, this gets confusing pretty fast when Shadowdancers get involved. Just what is "some sort of shadow", and where is it? Ask your DM. It's relative to the light, the position of the light source, the size of the thing casting the shadow, and the rules don't have anything to say on the matter whatsoever.

How big a shadow do you need to use it? Doesn't say. How much shadow is enough shadow to shadow jump? Doesn't say. How long is the shadow being cast by the enemy in front of me? Doesn't say. (This is probably why Pathfinder changed the wording on some of these abilities to be near "dim light" instead, which is more of a known rules thing than "some kind of shadow.")

As a DM dealing with a player who uses these abilities, it can get pretty confusing to try and sort out. It's actually easier in a dungeon with no light of its own, because if some player is carrying a light source, we can map it out on the board pretty easily relative to them and see where the shadowed areas would be (and which direction the player shadows are going, if you want to hide in the shadow of the Wild Shaped Druid).

But in an outside area at 5pm? Where are the shadows in that? It's a lot of work to sort out exactly how it all works, and it's often easier to come up with a simple rule of thumb and apply that rule of thumb consistently.

Hide

The one exception you mentioned is "how dim is dim enough?" In order to use Hide, you need concealment. Shadowy Illumination provides that. So you need to be in Shadowy Illumination, which is going to depend on what the area's light sources are (but most of those have a radius of providing light, and the table in the first link I provided has those distances).

You also need to be not being observed. If they're watching you, even with Shadowy Illumination, you can't use Hide. "Watching you" basically means they can see you at all, because in D&D vision is omnidirectional: characters are looking in every direction on every turn.

That's part of what makes Hide in Plain Sight so good (with HiPS, you can use Hide while being observed).

Low-light vision lets you see color!

Within the 120' radius of a deep gnome's darkvision, he only sees in black and white without the presence of a light source. Within the radius of a light source, folks can see in color whether it's inside their darkvision range (if any) or not. Low-light vision doubles the radius of illumination from all light sources, thus doubling the range the deep gnome can see color around a light source. This is useful.

Low-light vision has great advantages in distance!

Low-light vision's range is not fixed, nor is it centered on the gnome: it simply doubles the radius of a light source, no matter where the light source is or what its radius. This lets the gnome see things which would be hidden to creatures with only darkvision. For example:

If a torch sconce (20' radius of bright illumination, but 40' for the gnome) is 200' away from the party, then a thief sitting 30' away from the torch can make Hide checks to avoid detection by both party members with normal vision and ones with 120' darkvision. However, that Hide check automatically fails against the gnome, for whom the thief does not have the benefit of shadowy illumination to hide in.