Celerons are basically Pentiums with the cache disabled or crippled, which makes them much slower for certain applications. No one ever believes me... 
I do, kinda:
specs-wise: celeron was a pIII with less L2 cache
specs-wise: duron is an athlon with less L2 cache
Some celerons are pIIIs with one bad cache line, others are pIII's with two good cache lines but one disabled as you quoted, but the newest top-of-the-line celerons are pIII's since the celeron now has the same size L2 cache as the pIII, and Intel has stopped
making marketing the pIIIs, replaced by the p4s. The pIIIs out there now are the ones still in the pipeline or in warehouses. The celeron and pIII were the exact same size, even though Intel could have made the celeron smaller (due to the smaller cache). A smaller celeron would have meant more chips per disk, and if the celeron was different than the pIII, Intel was stupid to waste the expensive silicon by not making the celerons smaller.
Now, as for Durons and Athlons, almost all durons were not athlons, unlike the cerelon/pIII. The duron chip is smaller size than the Athlon, and made at the older factory, while the Athlons are made at the new factory. However, not to waste an almost perfectly good athlon chip (except for part of the L2 cache), AMD also sold these as durons if they worked fine as a duron. However, this was a very small fraction of the durons, unlike Intel and the celeron.
However, to say the celeron is a "crippled" pIII is like saying a person 6 foot tall a crippled person because he can't go again a professional basketball player (most of the time).
It's more like saying a V-12 engine is a 6 banger if six of the pistons were broken/removed. Not full power, but probably could still outrace a 3 cylinder colt.
