Reduction

Reduction is an explanation of one thing in another’s terms where both exist. So we can understand mental states as brain states, as identity theory or even behaviourism might say, though these are two different types of reduction (ontological and analytic)

An example of reduction is water to H2O. Both of them exist but we can reduce water to h2o and talk about water entirely in terms of h2o and perhaps even gain a more in depth knowledge and understanding of water, but they both exist.
This is an elimination so “water does not exist”
Reduction still leaves the reduced in existence
The key thing to understand about eliminative materialism, as in its name, is it is not reduction, it is elimination.
Identity theory (reduction) —> Mental states exist but we understand them only as brain states.