[jquery] jQuery class within class selector

is just going to look for a div with class="outer inner", is that correct?

No, '.outer .inner' will look for all elements with the .inner class that also have an element with the .outer class as an ancestor. '.outer.inner' (no space) would give the results you're thinking of.

'.outer > .inner' will look for immediate children of an element with the .outer class for elements with the .inner class.

Both '.outer .inner' and '.outer > .inner' should work for your example, although the selectors are fundamentally different and you should be wary of this.