they mean the same thing

The difference is very sublte. Both meaning you are somewhere else other than where you live. The addition of the preposition, "at" emphasizes that you are not physically at the place. Another example, "I am at the palace" vs "I am in the palace". The first one indicates that you are in the vicinity of the palace, you can also be inside. The 2nd one clearly indicates you are inside it and not around.

The do mean the same, but the former is just a very informal way of speaking. If the person listening to you is a native English or long-time ESL speaker, then he or she would have little to no problem putting your reply into the proper context. Q: Are you are home? A: I'm not at home Q: Are you are home? A: I'm not home ["right now." - will be understood] The preposition "at" is used to indicate presence or location, so both Andre and Ahmad above are correct in choosing "I'm not at home." It is the more grammatically correct or proper one. However, their logic as to why one can't say "I'm not home" is also wrong. No one who says "I'm not home" is equating himself (or herself) to a house. #1: [calling #2] Phew! I'm really glad I caught you at home... #2: What? I'm not home. This is my cell phone! [again, leaving out "at" would be understood and in this instance, "home" was used instead of "there"...] This is the way many people say things, so students need to understand that this is the way English is, at times. I hope this helps! (and apologies for the soapbox lecture...)

For a native English speaker, home and house are two different things. A home is the house in which you live. While we would say, Do you own a home? or Do you own a house?, we would never say Are you at house, this is incorrect. We would say, I'm not home, and omit the at. The "at" is understood. In everday speech, we often include at, even though it is not necessary and some would say wrong.

I share my view with Andre, we can't say " I'm not home " because a man can't be home ! the second sentence is the right one.