Bit Rate from Baud Rate

Baud counts symbols per second. Bit rate counts bits per second. They are equal only when each symbol carries exactly one bit, which stopped being true for serious links in the 1960s. A V.32 modem ran 2400 symbols a second with 16-QAM, four bits on each symbol, and delivered $2400 \ imes 4 = 9600$ bit/s. Calling that "9600 baud", as everyone did, was wrong by a factor of four.

The reason to pack bits into symbols rather than sending them faster is Nyquist. A 3 kHz telephone channel physically cannot carry more than 6000 symbols a second, so once you are at the bandwidth limit the only remaining move is to make each symbol mean more. That is what the whole modem era was: 300, 1200, 2400, 9600, 14400, 28800, all squeezed through the same 3 kHz by adding constellation points. Bits per symbol is $\log_2 M$, so 16-QAM gives 4, 64-QAM gives 6, and 1024-QAM in modern Wi-Fi gives 10.

Every extra bit per symbol packs the constellation points closer together, and closer points need a better signal-to-noise ratio to tell apart. Roughly speaking each additional bit per symbol costs about 6 dB, which is the same 6 dB per bit that shows up in converter resolution and for the same underlying reason. That is why a Wi-Fi link drops from 1024-QAM to QPSK as you walk away from the access point: the radio is trading bits per symbol for the SNR it has left, and the rate falls in steps rather than smoothly.