What does Atticus say God is? How is this different from what foot-washing Baptists believe?

From what I can see, you are referring to what Scout says about her father's definition of God in Chapter 5. In that chapter, Scout and Miss Maudie are discussing religion.
According to Scout, her father's definition of God is "loving folks like you love yourself." This corresponds with the Golden Rule, where we treat others the way we would want to be treated. Atticus' definition of God and true religion, however, differs from that of "foot-washing Baptists."
If we refer to the text, Miss Maudie defines "foot-washing Baptists" as legalists who strictly adhere to the letter of the law. According to Miss Maudie, foot-washing Baptists are "literalists": they are so focused on the academic definition of morality that they forget to display the true spirit of good religion. To Miss Maudie, foot-washing Baptists are so busy "worrying about the next world they’ve never learned to live in this one."
For his part, Atticus is first and foremost concerned with the Golden Rule. In Chapter 11, he tells Scout why he is defending Tom Robinson.

"This case, Tom Robinson’s case, is something that goes to the essence of a man’s conscience—Scout, I couldn’t go to church and worship God if I didn’t try to help that man.”

Atticus is primarily motivated by his conscience. He defends Tom because he believes that it is the right thing to do. To Miss Maudie, such a person is closer to God than literalists such as Stephanie Crawford.