The distinction is clearer if you focus on the place where there is a brane: there's an object there, with an energy density and having various charges. Then off the brane is just "space", but OK, you're asking what can be found in this space. The answer is that along with gravity, there can also be various electromagnetism-like "fluxes" or "form fields" for which the brane is a source. (These are distinct from the Yang-Mills fields - like in QED, QCD... - which are confined to the brane and which arise from strings whose ends lie on the brane.)
We should distinguish here between the situation in string theory, and the situation in a broader class of brane models. There are papers out there which just say "let there be branes, and fields on them and fields outside of them", and undoubtedly many of them are doing it in a way that's impossible in string theory. Then there are brane models which fit within the framework of string theory. Those are the ones I'm talking about.
Apart from having to obey specific rules, in the stringy models you can keep asking deeper questions like, what exactly is a brane, and how do strings create the space off the brane. And those questions don't have final answers yet, but there are all sorts of extra mathematical details which suggest that at the bottom there's going to be a new perspective, perhaps one in which both matter and space are "emergent" from some other ... thing. :-)
Obviously that new perspective would have implications for how to answer your question, but we don't have it yet, just mathematical studies like AdS/CFT, in which string theory in an "AdS" space is entirely equivalent to a field theory in a flat space with one less dimension. In that case, the strings, the branes, and the extra dimension all correspond to aspects of the equivalent field theory. We know lots of the math of this, but the conceptual interpretation isn't clear, at least it's not clear to me.
The real world isn't AdS. It ought to have an analogous (though perhaps more complicated) holographic dual description, but in this case we have neither the math nor the concepts! Well, we have "dS/CFT", which might be part of the math, but which is still in a very primitive condition compared to AdS/CFT... This has gone way beyond your question, so if you want a simple answer, the answer is that in string theory, the space outside the branes can contain these form fields ("fluxes", see e.g. "flux compactifications"), and gravity-like interactions and their fermionic partners (gravitino, dilatino).