A is established, then B is established, A is a sufficient condition for B, and B is a necessary condition for A;

B is established, then A is established, B is the sufficient condition of A, and A is the necessary condition of B.

It's that simple. The rest is the combination:

If A holds, then B holds, while B holds and A does not, then A is a necessary and sufficient condition for B;

A is established, then B is established, then A is established, then A is a necessary and sufficient condition for B;

B is established, then A is established, while A is established and B is not, then A is a necessary and sufficient condition for B;

B holds, A does not hold, A holds and B does not hold, so A is neither sufficient nor necessary.

The reason why you are confused is that you push B with A, which is sufficient and necessary. The concept you wrote is correct. People speak separately, so they all use A to push B instead.

When you are on the same topic, you can't blindly push A to B, which is different from the concept. Not separately, but in the same topic. So you should push A to see adequacy and B to see necessity.