Short answer: A grandfathered plan is one that existed before the ACA (March 2010) and hasn’t changed much, so it’s exempt from some ACA rules. ‘Grandmothered’ (transitional) plans were sold just after but are also allowed to continue under limited federal/state extensions.
Grandfathered plans were in place on March 23, 2010 and have avoided significant benefit cuts or cost-shifts, which lets them skip certain ACA requirements (like covering all essential health benefits or some preventive mandates), though they still must follow rules like dependent coverage to 26. ‘Grandmothered’ or transitional plans were issued shortly after the ACA and have been allowed to renew under repeated federal extensions adopted by many states. Both are shrinking categories; if you have one, compare it carefully against current ACA plans, since it may lack some protections.