``baud'' and ``bps'' are perhaps one of the most misused terms in the computing and telecommunications field. Many people use these terms interchangeably, when in fact they are not! bps is simply the number of bits transmitted per second. The baud rate is a measure of how many times per second a signal changes (or could change). For a typical serial port a 1-bit is -12 volts and a 0-bit is +12 v (volts). If the bps is 38,400 a sequence of 010101... would also be 38,400 baud since the voltage shifts back and forth from positive to negative to positive ... and there are 38,400 shifts per second. For another sequence say 111000111... there will be fewer shifts of voltage since for three 1's in sequence the voltage just stays at -12 volts yet we say that its still 38,400 baud since there is a possibility that the number of changes per second will be that high.
Looked at another way, put an imaginary tic mark separating each bit (even though the voltage may not change). 38,400 baud then means 38,400 tic marks per second. The tic marks at at the instants of permitted change and are actually marked by a synchronized clock signal generated in the hardware but not sent over the external cable.
Suppose that a "change" may have more than the two possible outcomes of the previous example (of +- 12 v). Suppose it has 4 possible outcomes, each represented by a unique voltage level. Each level may represent a pair of bits (such as 01). For example, -12v could be 00, -6v 01, +6v 10 and +12v 11. Here the bit rate is double the baud rate. For example, 3000 changes per second will generate 2 bits for each change resulting in 6000 bits per second (bps). In other words 3000 baud results in 6000 bps.
The above example is overly simple. Real examples are more complicated but based on the same idea. This explains how a modem running at 2400 baud, can send 14400 bps (or higher). The modem achieves a bps rate greater than baud rate by encoding many bits in each signal change (or transition). Thus, when 2 or more bits are encoded per baud, the bps rate exceeds the baud rate. If your modem-to-modem connection is at 14400 bps, it's going to be sending 6 bits per signal transition (or symbol) at 2400 baud. A speed of 28800 bps is obtained by 3200 baud at 9 bits/baud. When people misuse the word baud, they may mean the modem speed (such as 33.6k).
Common modem bps rates were formerly 50, 75, 110, 300, 1200, 2400, 9600. These were also the bps rates over the serial_port-to-modem cables. Today the bps modem-to-modem (maximum) rates are 14.4k, 28.8k, 33.6k, and 56k, but the common rates over the serialPort-to-modem cables are not the same but are: 19.2k, 38.4k, 57.6k, 115.2k. Using modems with V.42bis compression (max 4:1 compression), rates up to 115.2k bps are possible for 33.6k modems (230.4k is possible for 56k modems).
Except for 56k modems, most modems run at 2400, 3000, or 3200 baud. Even the 56k modems use these bauds for transmission and sometimes fall back to them for reception. Because of the bandwidth limitations on voice-grade phone lines, baud rates greater than 2400 are harder to achieve, and only work under conditions of good phone line quality.
How did this confusion between bps and baud start? Well, back when antique low speed modems were high speed modems, the bps rate actually did equal the baud rate. One bit would be encoded per phase change. People would use bps and baud interchangeably, because they were the same number. For example, a 300 bps modem also had a baud rate of 300. This all changed when faster modems came around, and the bit rate exceeded the baud rate. ``baud'' is named after Emile Baudot, the inventor of the asynchronous telegraph printer. One way this problem gets resolved is to use the term "symbol rate" instead of "baud" and thus avoid using the term "baud". However when talking about the "speeds" between the modem and the serial port (DTE speed) baud and the symbol rate are the same. And even "speed" is a misnomer since we really mean flow rate.