I'm writing a reply right now = This is what I'm currently doing. I'll write a reply right away = I will do this in a minute (immediately). Hope it helps a bit!

I agree with Truman, because as a native speaker, I think the difference is so small, that no one would even notice. Nothing personal, Sara! Ilene

I wouldn't say there's any difference. A distinction without a difference, as we say. I use them interchangeably without ever thinking about it.