Anastacia
I think Strength is referring to the internal battle, while the 9 of wands refers to the external battle. Both are Fire cards. Strength is an 8 rather than a 9.
So the person seeing you as Strength sees you as struggling with your own issues/weaknesses/desires and could be aware that it takes a lot of courage for you to speak up for yourself. They may also think that you are still in a position where you could be influenced one way or another.
The one seeing you as 9 of wands doesn't see that inner struggle. They see the external. They may see that you stand your ground and are defensive, but they don't appreciate your internal struggle. As far as they are concerned you have decided, you are standing your ground and you won't accept advice or be influenced.
So the person seeing you as Strength sees you as struggling with your own issues/weaknesses/desires and could be aware that it takes a lot of courage for you to speak up for yourself. They may also think that you are still in a position where you could be influenced one way or another.
The one seeing you as 9 of wands doesn't see that inner struggle. They see the external. They may see that you stand your ground and are defensive, but they don't appreciate your internal struggle. As far as they are concerned you have decided, you are standing your ground and you won't accept advice or be influenced.