I've heard this question, often phrased simply as a statement of truth, many times. I'm glad I can have this conversation once in a while. For the direction of my answer, I am thankful to my friend Dr. Adam Francisco, of Concordia University Chicago, who helped me sharpen my thinking.
We really need to get the person asking the question to do a little explaining. "What do you mean by 'just the same'"?
The usual answer has something to do with there being just one deity and being a religion with a strong ethical code.
When presented with that answer, there are a few places we don't want to go immediately. Those are places which will instantly provoke anger and end all interaction. But there are some directions we can take the conversation which can make the exploration work.
Christianity has a moral code. We want to recognize and embrace that. However, the moral code isn't at the heart of Christianity. What is at the heart of Christianity? Jesus the Christ, the second person of the Trinity, who has died to pardon our sins.
We probably don't want to ask a big huge question in return, but if we did want to do so, it would be something like this. "Are you saying that Islam and Judaism confess one God in three persons, Father, Son, and Holy Spirit, and that they say God in the person of the Son, Jesus, gave himself to take on a human nature, to suffer, and to die for the sins of the world, then rose again from the dead to show you that you will also rise to eternal life if you believe in Him?"
Like I said, that's a loaded question. It's too big. But it describes Christianity and can never describe Islam or Judaism. If you believe what that question set out, I have reason to think you're a Christian.
The big question also shows a distinction from all the non-Christian religions. It is set apart because of the nature and actions of God.
For about 2,000 years, Christians have confessed this and many have believed in Jesus as their life and salvation.
I hope my non-Christian questioners will believe in him as well. He is the only one who is victorious over death itself on their behalf. His name is the only name which can be believed on to give eternal life. So we embrace the distinction, and gently call people to recognize who the Christ is and why his work is central to all of life.