ASME B16.5 or ASME B16.47 contain definitions of class, pressure rating,, and pressure-temperature rating.
"Pressure Rating Designation
Class, followed by a dimensionless number, is the designation for pressure-temperature ratings as follows:
Class 150, Class 300, Class 600, Class 900 etc..
"Pressure-Temperature Ratings
Pressure-temperature ratings are the maximum allowable working gage pressure...at the temperature shown in Tables...for the applicable material and class designation..."
Rating is the qualifying parameter.
Class is a designation or name for rating.
The pressure classes were originally designated as “pound”, that is, Class 150 = 150 pound flange. The relationship between pressure class and rating for flanges is a complicated one and is defined in ASME B16.5. For most carbon steels, the rating of a Class 150 flange is 285 psi at 100 F. Similarly, the rating of the Class 300 flange is 740 psi. For threaded and socket welding fittings, the relationship between pressure class and rating is found in ASME B16.11.
it is important to recognize that a Class 150 (150-lb) flange is not rated for 150 psig at the same temperature that a Class 300 (300-lb) flange is rated for 300 psig, etc. That is why it is necessary to look at the Pressure-Temperature tables. Do not make an assumption about what the flange class will be without checking the tables. Note that the ratings also change when the flange material changes.
For example, if you want a standard carbon steel A-105 flange for a design pressure of 100 psig and a design temperature of 400 deg F, you will need to use a Class 300 flange. Many of us might assume that a Class 150 flange was acceptable if we were not familiar with the rating tables.