Here is the difference: Regardless is a real word while irregardless is not.
Some may protest that irregardless is a word because it is listed in respected reference sources, such as Merriam-Webster Dictionary and the Oxford English Dictionary. But if you look closely, you will see that it is defined as non-standard or incorrect use. Since regardless means "without regard," or "despite of something," adding the negating ir- prefix to it would create a double negative. This puts it in the same category as ain't.
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