I have seen some really great screencaps of pets that actually look like they have fluffy fur, like in this post, but no matter what I do with my graphics settings I can't seem to get that to display in my game. What setting do I need to adjust and where do I put it?

I put my system specs bellow in case maybe it is because my computer isn't compatible with that setting.
The diagnostic report didn't have an output for my sound (maybe because my pc has no built in speakers?) so I included the "Speakers" report instead.

If you had scrolled down you would have seen that the dogs required the curls markings/HD curls which is probably a CC item and there's 2(?) different ones the one from silver dragon estate and Brimwood estate.

Obviously the ability of your graphics chip will affect the fur definition. But also the fur will look 'fluffier' on longer hair, and the fur density and curl will affect this too. You need to be in Fur Shape>Advanced Mode to change these.

Thank you for your screen caps. I guess my graphics card doesn't support it because I have tried adjusting those settings and it only draws the fur on a smooth body rather than rendering the fur. Kinda sad when my sims 2 pets look better than my sims 3 pets in terms of the shape of the fur.

Sometimes it looks a little odd in my game; as you can see in this image there is a 'ghostly' outline (some kind of alpha/ render error?) on the edge of the fur:

So for some shapes and coat colours I have problems. Not sure if there's a way to get rid of that! I think your graphics chip is internal- so it shares memory- which might mean that Sims 3 puts it onto lower quality rendering.