Kerf is the width of the slot the saw cuts.
Plate is the thickness of the actual saw blade disc at the hub. The kerf will normally be larger.
In a blade like Fred uses, the teeth cut a slot nearly the same size as the blade thickness. That particular blade has teeth with a high angle on then to act like skew chisels. Each tooth is alternately angled left and right, so the cut is made extremely smooth. I don't know that I have ever heard them called zero kerf blades, but I do see them called thin kerf blades. I looked up the kerf and it is .098" with 15 degree angled teeth.
The main reason the kerf is normally larger is that will make the blade only touch the wood at the very perimeter. This reduces friction ( which robs power) and reduces burning. It does somewhat increase tearing of the fibers, so the cut may be slightly coarser.
The biggest difference between the blade Fred and I use and some other blades is the shape and angle of the teeth. Blades can be made to cut cleaner by having sharp sides as well as the top, or faster cutting by just cutting the wood from the top. This is largely the difference between a rip blade and a cross cut blade. Most folks just use one blade for all things, but you should get the blade that fits the most of your cutting tasks.
The larger the kerf, the faster and cleaner they cut. This is insignificant on many woods, but woods like curly maple will burn really badly if there isn't enough kerf clearance difference between the kerf and the plate.
You get what you pay for in these high end blades. Use a $15 construction blade for copping up big boards, and put on the Freud for the cuts that matter.