I just took a couple of minutes to figure out how baud translates to kbps. Turns out, it doesn't.
Back in The Day, 300 baud translated to 300 bits per second, but "as modem technology advanced, compression and other techniques were able to get higher bit per second transfer rates without a corresponding linear increase in state changes. Baud became an outdated term because it wasn’t able to accurately and proportionately express transfer rates, so bps became the standard."[0]
There is some more in-depth information about what "as modem technology advanced" means on Wikipedia[1]. Interesting stuff.
rbanffy and ordinary are both right. "Baud" is the number of symbols per second; a symbol can be a specific frequency, or a phase shift, or Complex Electronic Magic. Up through 300 baud, each end used a tone for 0 and a tone for 1, and that was it. One bit = one symbol. (You could hear zeros and ones go by if you listened, and for Commodore owners, it was critical to be able to whistle the answer tone so you could trick the modem into hanging up - it auto-answered every call.)
So each baud carried one bit, and we got used to equating 300 baud with 300 bps. Then came 1200 bps modems, which sent two bits per symbol (four discrete tones, IIRC); they were technically 600 baud modems. It got more complex from there. And thus the confusion began; trying to tell people they had a 600 baud modem was about as useful as trying to tell them it's really called GNU/Linux.
Back in The Day, 300 baud translated to 300 bits per second, but "as modem technology advanced, compression and other techniques were able to get higher bit per second transfer rates without a corresponding linear increase in state changes. Baud became an outdated term because it wasn’t able to accurately and proportionately express transfer rates, so bps became the standard."[0]
There is some more in-depth information about what "as modem technology advanced" means on Wikipedia[1]. Interesting stuff.
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[0] http://www.tech-faq.com/kbps.html
[1] http://en.wikipedia.org/wiki/Baud