i've had to explain this god knows how many times; i'm surprised some of the information i give is never a sticky.
anyways...
First thing to remember is that theoretical values are places on every box. In other words these are what your graphics processor *should* be able to push if all conditions are perfect.
Now 34 million triangles/second (game polygons) would be a value taken from untextured, unshaded, non transform and lit polygons.
However Vertex do not have any of the processing hang-ups that dog triangle rendering, which means the theoretical value on the box is basically what your processor can do. (no matter what)
When we get into ... there must be 3 vertices per triangle, technically this is true. Which would mean you could say the theoretical maximum polygons for an 84 million graphics card would be around 28 million.
Unfortunately not every single polygon will have it's own triangle set.
So if you take a simple Quad (DB Plain) for example.
You could have 2 Triangles + 6 Vertex. However it is more common for vertex to be shared when there is no need for multiple UV coordinates, thus meaning: 2 Triangles + 4 Vertex.
When you get into a cube you will always have 12 Triangles, however you can have between 8 and 36 Vertices.
Vertices control a lot of your meshs' attributes; UV Points, Colour and Normal Light Index are the normal stuff. So really how many vertices your card can push is getting more and more important.
Particularly as Shaders work per Vertex NOT per Triangle.
Really there is no way to technically compute between the two i'm afraid. This said, DarkBASIC Professional is not as fast as DirectX/OpenGL natively. So don't think your card is capable of pushing anywhere near to what the box states.
an example is ... in DirectX GeForce FX 5200 @ 250 MHz can push:
1,200,000 Triangles / Scene (72,000,000 / Second)
1,380,000 Vertices / Scene (83,000,000 / Second)
under DarkBASIC Professional the same test:
650,000 Triangles / Scene (39,000,000 / Second)
750,000 Vertices / Scene (45,000,000 / Second)
(a per scene value = 60FPS as this is VSYNC and what is considered standard rendering speed 640x480x16 60Hz being the most compatible visual setting)
And remember you don't even have to attach Vertices to anything, which allows them to be used as template position holders (which is a common practise in alot of games)
As for Texels... these are the name given to sub-pixels.
When your scene goes for rendering your often get 4:1 Texel

ixel ratio. Texels are combined in many ways to render 2D, the more Texels that can be passed the faster the 2D effects are in your card.
Particularly Multi-Texturing. (this can also in many regards contribute to your texture rendering speed on mesh)

Athlon64 FX-51 | 1.5Gb DDR2 PC3400 | GeForce FX 5900 Ultra 56.60 | DirectX9.1 SDK | Audigy2 | Windows XP 64-Bit