The placards said, “This aircraft is ‘G’ rated” or “This aircraft is ‘H’ rated” and they referred to the engine thrust rating. We had to check that the FMS engine rating was the same as on the placard. BA had a mixed fleet at the time, and they were worried that an FMS or engine could be re-fitted after repair that was incompatible. Intermix flying with two different ratings was not allowed.
The Rolls Royce RB211-524G had about 56,000 lbs of thrust and the 524H had about 60,000 lbs of thrust at seal level (if memory serves). I believe it was a fairly simple tweak of the EEC plus a pin change for the FMS which decided which rating was available.
From about 2008 all engines on the fleet were de-rated to ‘G’s but the sims were all ‘H’s! Didn’t really make much difference in the grand scheme of things.
Another mod introduced was the ‘Trent Core’, which reduced EGT and Fuel burn. Those engines were 524G/T or 524H/T.
Hope this explains what you were asking about.