Besides imposing less strain on the saw motor, thin-kerf blades waste less
wood. If you are cutting big pieces of inexpensive material, thick kerfs
are not a problem. However, if you are ripping 1/2"-wide strips (which I
do sometimes), a 1/8" kerf is wasting 20% of your wood! At $4/bf +/- for
hard maple, that makes me pay attention!

I don't know about the Diablo blade, but you noticed that the model numbers
were different between Home Despot and the web. It's not uncommon for
manufacturers to make a "special" model for clients who buy a lot of their
product, thus you might find an item at Home Despot which is apparently
identical to one at Lowe's, but they different model numbers. I believe
this is to reduce price-guarantee claims. You might go to Home Despot and
say "I saw the same one at Lowe's for less!", but HD would say, "Diff'rent
model numbers, different items. No Deal".

--
John Snow
"If I knew what I was doing, I wouldn't be here"