The numbers are: 9 petahashes/second (entire Bitcoin network [FTA]), and 20 petaflops/second (IBM Sequoia [1]). If you equate a SHA-2 hash with a floating point op, the ratio is 0.45, not 4,500.
This site (http://www.bitcoinwatch.com/) seems to do a 'flops' type conversion from the hashrate on the bitcoin network.
Currently at 108239.28 Petaflops which is 5400x the performance of the IBM Sequoia. This is approximately the quoted amount of 4500. While I don't agree with the idea that a hashrate can be converted into flops because its more bitwise opts others are drawing similar calculations to UCSD.
You are making a terrible apples vs. oranges comparison.
A bitcoin hash is about 1900 32-bit integer operations [1]. This is comparable to 1900 32-bit floating point operations, not one(!). Because most CPU/GPU, when they can execute N integer ops per cycle, can also execute N floating ops per cycle.
So the ratio clearly is in the ~1000 order of magnitude.
"A bitcoin hash is about 1900 32-bit integer operations [1]. This is comparable to 1900 32-bit floating point operations, not one(!)."
That's the amount of work you do in a software implementation of SHA-2, running on a CPU or GPU. This abstracts the hardware complexity inside the chip, which is very relevant when we're going into ASIC's. SHA-2 is bit shifts, masks, and binary adders: it's much simpler than a floating point core.
A hardware comparison would be something like ops/(transistor * time). A recent Bitcoin press release [1] claims 500 billion SHA-2 hashes/second out of >1 billion transistors: ~500 hashes/(transistor-second). A 7990 has a peak throughput of 8.2 teraflops SP [2], out of 8.6 billion transistors: ~1,000 flops/(transistor-second). Both are on 28nm processes.
A Radeon 7990 gets around 1.2 gigahash/second and 8.2 teraflops.
The ASICS are of course skewed towards hashes from there, and I guess the supercomputer could be more skewed towards floating point than the GPU, but a large factor seems more likely than a fraction.
[1] http://www.top500.org/system/177556