It is defined as: "an argument based upon an assumed similarity between two things, people, or situations when in fact the two things being compared are not similar in the manner invoked."
Okay, I'll try this out.
There are two men, both throw a stick to the ground and it becomes a snake. Both claim that their God empowered them to do this.
Using this event alone, which man was using Magic and which performed a Miracle?
You claim that the similarity between the two things being compared are not similar in the manner invoked.
So how are the two different?
Both performed a supernatural event with the help of a spirit creature. Is the only diferentiator between what is considered magic and what is considered a miracle who performed it? Because that is exactly what JWFacts states: "the Bible shows that God's followers practice magic, even if they are usually referred to as miracles"
If you cannot differentiate between magic and a miracle until you learn who performed it, that is not a logical fallacy, that is doctrine.