What is the difference between believing that God doesn't exist and not believing that God exists?

Well...

the difference is in the (unmentioned) details.

-- I believe that God does not exist.

leaves no room for alternatives. The person is convinced that God does not exist. Period.

-- I do not believe that God exists.

can have the same or different meaning from the previous, depending on the details. For example:

A - I do not believe that God exists. However: I believe that it is possible that God exists. I just have not found sufficient reason to be persuaded that he does. [agnosticism]

B - I do not believe that God exists. Indeed: I do not believe it is possible that God exists. [atheism, and note: this is equivalent to "I believe that God does not exist."]

So:

-- I do not believe that God exists.

is more vague than the other

can mean the same thing as the other (i.e. atheism)

or something else (i.e. agnosticism)

basically, jews,buddhists,muslims pray head down to satan. during the night christian earthlybowdowns count 40 times more than daily earthlybowdowns. since, most of the time witches pray during the night against christians, it's best to pray at night ...maybe you could do 2000 christian earthlybowdowns.. notice that muslims-jews-buddhists stay head down which shows that they worship satan; christians have to get up super fast showing allegiance to Christ and not the devil. so, christian earthlybowdowns: u face east, legs together (so that demon don't run underneath ur legs); u look at the eyes of icon (energy goes ur way according to saint Pelageya of Ryazan); u make proper Orthodox sign of the cross (first three fingers together as if u had a pinch of salt in them; thumb always straight; ring and pinky to palm; firmly touch forehead: "in the name of the Father"; firmly touch 1cm above belly button: "and of the Son", raise hand to chest level and now move to right shoulder where there bones meet: "and of the Holy"; move to left shoulder: "Spirit. Amen"; release the fingers; hand down by ur side); u bow down on ur knees (knees together), then put hands together on the floor, then forehead on top of backofhands; as soon as ur forehead touches the back of hands, get up super fast showing allegiance to Christ (and not the devil). do 2000 times during the night against witches. 'cuz witches work hard for satan (by praying like three hours); you have to show them respect by outworking them; u feel me? but of course when u tired u could pray the Jesus prayer at least three times every hour (don't sleep 4 more than 1 hour; wake up and pray the Jesus prayer three times; then u can rest a little bit; in case witches pray real hard to satan, then u have to pray to Jesus as many times as possible); thank u; forgive me rudeness.

You error in that it is "gods". "not" you left out the not.

“I believe God doesn’t exist” means “I conclude, based on the evidence, that God does not exist.”

“I’m not believing that God exists” leaves a little room for: “I will consider evidence presented for the claim that God exists.”

First, I think we need to lay a baseline.  Agnostic is not mutually exclusive with theist or atheist.  

Theist/atheist is a question of belief, of whether someone has a belief that a god or gods exist. So, if somebody isn't a theist, they are an atheist. That's what that word literally means. A- (not) theist.

Gnostic/agnostic is a question of certainty in knowledge, about whether someone claims their believe is a known fact.

So, for example, I don't believe you've got a million dollars in your wallet. But, I haven't opened your wallet, so I don't claim this as something I demonstrably know. Knowledge and believe are septate questions.

One can be:

Gnostic theist

Gnostic atheist

Agnostic theist

Agnostic atheist

These pairings aren't mutually exclusive.

So, as it comes to your question, the answer would be they're both atheists.  They both are without a belief a good exists.  One is agnostic atheist, the other gnostic atheist.

One involves

an unsupported, emotional certainty,

and the other does not.

Stating that it is a fact

that God doesn't exist

is a claim about external reality.

Stating that one believes that God doesn't exist

is information about a state of mind

that involves an unsupported, emotional certainty..

Stating that one does not believe

that any God exists

is information about a state of mind

that does not involve

an unsupported, emotional certainty.

--

Regards,

John Popelish

"Believing that God doesn't exist" implies that there is some reason to at least suspect that God might exist, basically, except for the negative, it is a belief just like "believing that God exists".  On the other hand "not believing that God exists" is the same as "lacking belief in God".  It's a subtle difference

Edit:

I think bringing in the terms agnostic, atheist and theist clouds the issue, for example a theist could believe in some god or gods, while still believing that God did not exist - this might be a stretch, but is still entirely possible.

I also don't think that either say anything about how open one is to evidence except that "believing that God does not exist" is a belief and beliefs rarely change due to evidence,  while "not believing God exists" suggests that nothing compelling has been encountered to cause any sort of belief.

In any case, you could use either one in everyday conversation, unless you tried to claim that as an atheist I "believe that God does not exist", because I would reply that that means I'm not an atheist, I simply lack belief in all gods, or I don't believe that any gods exist -- again a very subtle difference, but a profound one.

People that actually believe that God exists have proof in their life. Their financial circumstances improve their relationships improve their legal affairs improve their credit score improves.

If or if not an actual God is doing this cannot be proven one way or the other.

What can be proven is that the belief in God is helping these people. And since it's helping so many millions and millions of people people keep on believing in God

In the common American parlance, the first would be an "atheist" (one who feels sure God doesn't exist), and the 2nd would (usually) be an "agnostic" (one who isn't sure whether God exists, and allows it's possible).   Americans typically don't multiply categories into 5 or 6 different varieties, for instance, and here only have 3 common ones: believer, atheist, and agnostic.  These 3 are all the categories that 97% of people ever use, and most won't willingly add any more.

"God doesn't exist" is a claim.  

"Not believing God exists" is a rejection of a claim.  It is not a claim itself. 

I reject the claim that God exists because I find no evidence for his existence.  I do not make the claim that he doesn't exist, because I remain open to evidence.