Yes, there is a difference between "God" and "god".
Not all languages have this problem. As an example, in Arabic the word for God is Allah, and the word for god is illah. This makes matters confusing for English speakers as God and god have the same pronunciation, and using "god" at the beginning of a written sentence makes it look like God.
So capital "G" God means "Ultimate Reality" or "Supreme Being" depending on the dictionary. They both mean the same thing.
It is not surprising that you have never heard this definition because the vast majority of people, theist, atheist, or otherwise has a superstitious conception of God.
So really, denying God is not a reasonable position. Instead it is more fruitful to debate about what God is, what God isn't, the nature of God, etc.
Because when someone is an atheist towards this particular God, they are denying truth and reality. I don't really believe that most atheists are aware of this, but that is actually what their position means. I think it would also be interesting to note that Christians were called atheists back in ancient Rome, an identity that most people today would consider to be ludicrous to attach to a Christian.
The Monotheist God is The Ultimate Reality. This is true in certain sects of Hinduism, Islam, Judaism, Christianity, etc. The concept is even present in Buddhism, Taoism, and just about any tradition on the planet.
And though I myself identify as a Christian and have my theological education in that tradition, I must admit this is a universal concept.
So that is your good news for the day. The Ultimate Reality is God. That is something that transcends culture, tradition, conception, everything.
It Is What It Is.