Let me rephrase things then to see if I can make myself clearer.
Let's change "I believe God exists" to "I believe proposition X is true where X is 'God exists'".
By adding "not" and change true to false, we get four different scenarios:
1) I believe proposition X is true
This is theism.
2) I believe proposition X is false
This is strong atheism.
3) I don't believe proposition X is true
In the situation of weak atheism, the person can also neither believe proposition X is false.
He can simply don't know the real answer whether proposition X is true or not.
(A) Thus he don't believe proposition X is true until he got reliable evidence which this evidence prove proposition X is true.
(B) And he neither believe proposition X is false until he got reliable evidence which this evidence prove proposition X is false.
(A) and (B) is not mutually exclusive.
Don't believe X is true =/= believe X is false.
He only believe proposition X is false when he get reliable evidence which this evidence prove proposition X is false.
(a) Without convincing evidence which prove X is true, then he say: i don't believe X is true.
(b) Without convincing evidence which prove X is false, then he say: i neither believe X is false.
If a person have situation (a) and (b) present in him at the same time, then he say: i don't believe X is true, i neither believe X is false, it's because i don't know whether X is true or false. Still, i'll not believe X is true if i got no convincing evidence to prove X is true. And if i got no convincing evidence to prove X is false, it doesn't automatically means X is true, in order for me to say X is true it got to have convincing evidence to prove it's actually true first.
I hope what i said made sense, it have became a little confusing to me with the word "believe". If anyone find any error please feel free to point it out.
4) I don't believe proposition X is false
Don't believe X is false =/= believe X is true.
Don't believe X is false can be because the person got no convincing evidence to prove X is false.
But for the person to believe X is true, for him it got to have convincing evidence to prove X is true first.
Without evidence to prove X is false =/= with evidence to prove X is true.
Without evidence to prove X is false =/= X have already been proven true.
Without evidence to prove X is false can be the possible situation that the evidence is pending to be found.
The evidence to prove X is false, is pending to be found =/= X have already been proven true.
In order to say X is true it got to have convincing evidence to prove it's actually true first.
Also i'm not sure if this question is related to the things i've been said above, this question ---> "can we prove the existence of negative/non-existence doesn't exist in all situation?" .
Without evidence to prove negative/non-existence doesn't exist =/= negative/non-existence have already been proven exist.
Now, if X represents "God exists", then supposedly strong atheism fits 2) and3), and they're considered similar but equal
The same goes for 1 and 4, simply because let's change true and false to V. V can be true or false. That simplifies the list to:
i) I believe proposition X is V (where V is true or false)
ii) I don't believe proposition X is V (where V is true or false)
If X is "God exists" and V is true for i) and false for ii), is the same condition or relationship as if V is false for i) and true for ii).
In other words, implicit theism is just as different from explicit theism as implicit atheism is from explicit atheism.
I've already explain in the above why 1 =/= 4 and 2 =/= 3.