Models/geometry are created with arbitrary units; if those units happen to already represent meters, no scaling is needed, only translation is needed.
model-space coordinate (no units) * World = world-space coordinate (meters)
View-space units are the same as World-space. The View matrix translates and orients the world such that the new origin is the camera's location and the Z-axis points in the same direction as camera-forward. Coordinates are now relative to the camera; i.e. a coordinate that is "to the left" of the camera will have a negative X-value.
world-space coordinate (meters) * View = view-space coordinate (meters)
Projection-space units are intermediate; they represent a percentage of the active rendertarget/viewport. Projection-space is also defined with the origin at the camera's location, moving the camera to the center of the rendertarget/viewport. Coordinates are relative to the center of the screen and are in the range of -1 to 1; i.e. coordinates along the left-most edge of the rendertarget have X-values of -1 and coordinates along the bottom-most edge have Y-values of -1.
view-space coordinate (meters) * Projection = projection-space coordinate (unitless)
To convert projection-space coordinates into pixels, you convert them from the -1:1 range to the 0:TextureDimension range. Texture-space defines the origin, (0,0), at the top-left corner and (1,1) at the lower-left corner.
textureSpaceCoordinate = projectionSpaceCoordinate //-1 to 1
textureSpaceCoordinate += 1.0f; // 0 to 2
textureSpaceCoordinate /= 2.0f; // 0 to 1
//A Y-value of 1 corresponds to the top of projection-space
//and the bottom of texture-space; need to invert it
textureSpaceCoordinate.Y = 1.0f - textureSpaceCoordinate.Y;
//If the texture is 800 pixels wide, X-values will range from 0 to 799
pixelCoordinate.X = textureSpaceCoordinate.X * (TextureWidth - 1);
//If the texture is 600 pixels tall, Y-values will range from 0 to 599
pixelCoordinate.Y = textureSpaceCoordinate.Y * (TextureHeight - 1);
If you start the above process at Projection and use the view-space coordinate (1, 1), the resulting pixelCoordinate approximates the "PTM_RATIO"(s).