What is the difference between "appeal to ignorance" v "proving non-existence"?

When one appeals to ignorance, they are basically using their ignorance on something in support for their claim about that something. The classic example is saying that since we don't know that God does not exist, then that is evidence that he does. Of course, we can say the same thing about a 2-headed space clown that lives on the dark side of the moon.

Proving non-existence is a more specific example of the argument from ignorance, in that the "ignorance" is specifically characterized by the other party's inability to prove non-existence, and the claim is specifically one of existence. The above example fits this fallacy as well.

To differentiate the two, we can use a more general example of the argument from ignorance: There is no proof that genetically modified foods won't have disastrous long-term effects, therefore, they probably will. While this *might* fit under proving non-existence (the non-existence of "proof"), it is better described by the argument from ignorance.

A more clear example is when the ignorance is characterized by one's specific ignorance, rather than the absence of information from the general knowledge. For example, I don't know anyone who is gay and likes football, therefore, gays don't like football .