In a basic sense, they mean the same thing. They both tell you that the speaker is a human being. However, being "human" (without the article) can also mean experiencing the common emotions and life events that most people experience in human culture.
"It's only human to feel that way" means "it's completely normal to feel that way, because that's how most people feel." "Being human" can mean participating in human society, or having normal human flaws, desires, reactions, etc. "What can I say, I get angry sometimes. I'm human." (Meaning: it's normal to get angry sometimes.)
"I am *a* human" is more likely to refer to the species of humans in a scientific sense. "He's *a* human" probably means that he is literally a human being, not a dog or a fish or a tree.
("He's human," with no article, can *also* mean "he's a human and not any other type of creature." You would have to look at the context of the sentence to find out if "he's human" means he is literally a human being, or if it means he is a normal person who has normal human desires, faults, and so on.)