The fire class (A1, A2, B, C …) describes how a material behaves in a fire test: non-combustible, limited combustibility, combustible. The calcium silicate boards used on partition faces are A1; the waterproof composite board used behind tile is B1, which is combustible but difficult to ignite. Both are correct for their place, and neither can substitute for the other.
Smoke toxicity class (AQ1, AQ2 …) describes what the smoke does to people, not what the material does to a fire. A board can be B1 and still produce low-toxicity smoke. On escape routes the smoke class matters as much as the fire class, because most fire deaths are from inhalation, not burns.
Thermal stability (G1, G2 …) describes how the board behaves when it is heated: whether it cracks, shrinks or spalls. It matters on a fire board that is exposed to a rising temperature on one face for the rated period, because a board that spalls loses its protection before the time is up.
The assembly is what gets rated. A two-hour wall is a tested combination of boards, studs, fixings, joints and penetrations, tested as a whole. Changing the board thickness, the stud spacing, the fixing length or the sealant means the rating no longer applies, even if each component still has its own certificate. When a project asks for a rated wall, the answer should be a tested system report, not a board data sheet.