Are the statements "I don't believe God exists" and "God does not exist" logically equivalent?

I don't believe they are the same thing. One, as you pointed out, rests in ones personal opinion or belief while the other makes a statement of fact...one which logically requires proof since it is a statement of fact. (Double standards prove a lack of intelligence.)

"God does/does not exist" are positive claims and the makers must provide the evidence that God does /does not exist. Both are tough, but recall we're proving a proposition in maths class, we can see that the person that say "does not" may have more advantage because he only needs to prove just 1 aspect, one word, one thing about the proposition is not true, then the whole proposition failed. Meanwhile, the person that prove a proposition must prove that every single tiny bitty thing about the proposition is absolutely true in the required conditions.

While ppl that say "I believe/don't believe God exist" is just an opinion and a belief, that "I think so but it may not be true, however, I strongly believe it is". This may not true, but as a matter of faith, it needn't be proven wrong.

However, the line is not that clear

they are not equivalent.

Why is it that people have no problem if I say "Unicorns do not exist" but have a conniption fit if I say "God does not exist."

The evidence for God consists of the Bible.

O.K. there are questions that people push God into the answer for. But historically they have been very wrong about this, and the answer should really be "I do not know". So asking "Where did the universe come from?" is not evidence for God. There is no reason that "The unicorns did it." is a worse answer than "God did it." Both are baseless assumptions without evidence and both beg the question.

The evidence for unicorns consists of multiple reference in multiple books. (Not all written as fiction)

So the "evidence" for unicorns is directly equivalent to the "evidence" for God. But claims of non-existence are treated so very differently. Why is that?

A needs not be proven but B does and it is far from being proven( quite the opposite from the evidence provided)

To be logical either decision must have some assuring evidence according to the agent of the decision but B needs convicting evidence

They are not the same.

"God does not exist" requires that the person making the statement show some proof to support the statement. "I don't believe God exists," on the other hand, deals with belief, so requires not evidence, though evidence is always nice.

No. One is an assertion of personal opinion; the other is a statement of fact.

You cannot "plug" one into the other and produce the same result, therefore, they are not equivalent.

It's all in the semantics of the logic used. The statements lack the property of convertibility.

The first is a statement of opinion, the second stated as fact. There is a difference between them.

The second one would require substantiating evidence; the first is just a personal outlook.

I'm not sure what you mean by 'logically equivalent'. If you mean 'semantically equivalent', then no; one is a positive assertion, while the other is a responsive assertion. Additionally, one is a statement of (lack of) belief, while one is a statement of knowledge.

They are both statements of fact, only the second one requires the person making the statement to offer proof to support what they are stating a fact.. The first being statement of what that person believes. These are two different thing all together.

no, they aren't

follow up:

neither really, as one is opinion (opinion requires no further substantiation unless you believe the person is lying about it) and the other is a universal negative statement, which are impossible to substantiate... in the face of no contradictory evidence the two options would be agnosticism or the above statement

No, they are not. One is a statement of belief and the other a statement of fact. If something cannot be proven, it cannot be stated as fact. A person has a right to believe in whatever they want.