# ground terms in logic and $\lambda$-calculus?

What are the differences of ground terms in first-order logic and higher-order logic?

I found on the Wikipedia: "In mathematical logic, a ground term of a formal system is a term that does not contain any free variables."

That mentioned "free variable" is the same thing with free variables of $\lambda$-terms?

I know the closed terms and open terms $\lambda$-calculus. How can we connect closed terms of $\lambda$-calculus with ground terms of logic?

I am bit confused between these concepts, could anyone explain?