There's no such option in InDesign. (Perhaps it could be accomplished with a script, however.)
The difference is that InDesign uses pages and spreads and not artboards.
Illustrator shows multiple artboards on the same screen, and it would make sense that you'd want to select only either one, or all. InDesign normally shows one spread at a time (unless you're zoomed way back).
Well that's a shame Steve, in my mind 'a page, is a page, is a page' whether or not Adobe choses to call it an 'Active Artboard' :-) And the paradigm between the 2 apps is really very similar: pasteboard/page versus pasteboard/Artboard
But the fundamental issue is Illustrator gives me the choice, where InDesign does not :-(
I know this not much of a comfort, but after teaching the program since it came out (1999) and years on these forums, you're the first person I've heard who's made that request.
I'd suggest submitting it as a feature request. Be sure to make a good case for why you need that feature (because there are hundreds and thousands of different requests!)
Thanks for taking the time Steve, but a feature request submission falls in the realm of fantasy for me as I have no intention of moving beyond CS6 and my perpetual license! Just not interested in 'renting' software, whereby if I find myself in a position where I can't pay my rent I lose access to all MY files.
Might try the scripting forum
@Steve – If you ever get a request for selecting all page items on an active page or on all pages of an active spread, see my script here in answer #4:
A feature like that could be a boon.
When I was working at the script I discovered a strange thing I wasn't conscious of:
If you have an anchored object selected, "Select All" in the menu does nothing. At least it will not select anything additional to the selected anchored object.
That should change, I think…
(Another feature request ;-) )
In this case my script will deselect all and invoke the menu command for "Select All" (minus all objects on the pasteboard or on other pages but the active one).