The MAX31855 and MAX31856 have much of the same functionality but the MAX31856 has a few additional features which would be an advantage in industrial applications in particular.
The MAX31856 has on-board 50/60Hz noise filtering and +/-45V input protection whereas the MAX31855 does not. Both devices are thermocouple-to-digital converters for K-, J-, N-, T-, S-, R-, or E-type thermocouples, additionally the MAX31856 can also operate with a B-type thermocouple.
Tha MAX31855 has 14 bit resolution and an 8 pin SO package type, whereas the MAX31856 has 19 bit resolution and a 14 pin TSSOP package. Both devices are cold-junction compensated.