When is the bit rate and baud rate equal to each other?

Answer 1

I'll argue the point with "The goblin". He's confusing bits and bytes, a common error. Bit rate and baud rate are basically equal up to 9,600 bps/baud (with some exceptions, see below). Baud rate referrs to the data communications rate between 2 DCE endpoints (aka modems). Bit rate refers to the throughput between terminals (computers in modern parlance). On POTS dialup connections the maximum baud rate is 9,600 baud. Regardless of the bit rate, the baud rate will never be higher. Specialized encoding and compression allows for higher bit rates up to about 56kbps.

So, up to 9,600 you can generally use baud rate and bit rate interchangeably. Anything past 9,600 though and bit rate refers to your actual throughput while the actual baud rate remains at 9,600. There are a few exceptions to that though you'd rarely see them today. I do recall some government circuits that ran at 4,800 bps with an underlying baud rate of 1,200. That was back in the early to mid 1980s though when most modems capped at 300 or 1,200 baud and was considered pretty high tech in the day.

Answer 2

Short answer; Never.
The confusion is partly caused by the use of similar abbreviation for both.
A bit is one zero or one of digital data. A baud originally represented one digit or numeral. In rough terms there are 8 bits in a baud.
For data transferal purposes say over the Internet, there is also error correction to take into account which uses more bits.
As a rough guide we can then say for example that bauds = bits divided by 10.
Thus a 1Mega bit link provides a data rate of 100Kilobits.
All clear?