In digital messages, each character can encode one or more bits. Very simple modulation schemes, for example. PSK, just encode one bit per character, but more complex schemes can encode several bits per character, for example. QPSK encodes 2 bits per character. Therefore, the symbol rate (characters per second, aka baud) may be less than the bit rate (bits per second).
Chip rate is a term that is specific for communication with an extended spectrum - a symbol is represented by a number of chips, so the symbol transfer rate is lower than the chip speed.