ground terms in logic and $\lambda$-calculus?
I think you're basically correct. "Ground term" is more or less the same as "closed term".  Certainly the definition you gave is the same as closed term.  Personally, I don't think I've seen "ground term" used much for first-order logic or any system with binders.  The place where I most commonly see "ground term" used is universal algebra where there are no binders and so "ground term" means a term with no variables at all.

To be pedantic, the notion of "free variable" is used defined when defining the syntax of whatever formal system you're using.  As such, the notion is tied to the system being defined.  Conceptually, though, the it's the same idea.  In the last decade or so, there's been a lot of research in the CS community in capturing and manipulating binders in a languange-agnostic manner so that tools, libraries, and languages can be defined that allow easy definition and manipulation of languages with binders.  For example, the languange Beluga and the various "nominal" systems.