To answer your question.. you are correct. Just because you select 1920×1080 pixels for the ‘resolution’ does not necessarily mean that your render will have a 16×9 aspect ratio. The ‘pixel’ ratio value(s) that appear in the Render Settings dialog determine the overall aspect ratio. The default is 1:1 which gives you square pixels in the final render.
So.. If you choose a resolution of 1920×1080 and leave the pixel aspect ratio as 1:1, then you will get a 16×9 output. This is because 1920 div by 1080 is the same as 16 div by 9 (or 1.778). Thus, your settings have been working just fine because HD is natively 16×9 and happens to use square pixels.
As a comparison.. if you were working with DV footage that is natively 720×480 pixels, you would need to enter a pixel aspect ratio of 1.185:1 (rather than 1:1) to get a final render that is 16×9. Why? The DV video standard uses non-square pixels for display. The data is stored with a square pixel aspect ratio of 3:2 (720 div by 480) but is displayed with either a 4:3 or 16:9 aspect ratio. So.. to get a 4:3 image, DV pixels must be squeezed horizontally and to get a 16:9 image they must be stretched horizontally.
To determine the correct pixel aspect ratio for 4×3 DV footage, you divide the desired aspect ratio of 1.333:1 (that’s 4 div by 3) by the native (square) pixel aspect ratio of 1.5:1 (that’s 720 div by 480, or 3:2). This gives you 0.889:1.
Likewise, to determine the correct pixel aspect ratio for 16×9 DV footage, you divide the desired aspect ratio of 1.778:1 (that’s 16 div by 9) by the native (square) pixel aspect ratio of 1.5:1 (that’s 720 div by 480, or 3:2). This gives you 1.185:1.
BTW.. I think it’s best to set the ‘Film Format’ popup in the Render Settings dialog to ‘Automatic’ which basically turns this feature off. All C4D needs to know is the final resolution and the pixel aspect ratio. As far as I can tell, the ‘Film Format’ option is just a data entry convenience that forces the resolution you enter just above to be of a specific aspect ratio. But that is confusing because the ratio of width to height of the image is not necessarily the ratio that it will be displayed at. It is for square pixel formats (like HD) but not for non-square pixel formats (like DV).
Hope that helps. John