In impress, I have some elements which make sense for a presentation, but not on the PDF. Is there a way to mark elements as “do not export in PDF”? Or more generally, can I layout a slide differently for different target media? In other tools like LaTeX Beamer, this has been possible for the last decades.
AFAIK there is no straightforward way to do this for a presentation file.
In Draw you can use layers for this (layers in Draw work as logical grouping elements, rather than physical overlaying ; which layer an object is put on does not have any bearing on “stacking order” for that object).
For each layer, you can select whether objects should be visible and whether they should print. (Right click layer tab to edit settings)
In general, settings for print also apply to PDF export. Can’t test right now whether this works for PDF export. If it doesn’t, there is always the route through PDF “virtual print”.
I prefer Draw anyway, when presentation is a backdrop for talk. More direct interface and less bling to drag attention away from the subject. For unattended presentations, Impress is the tool of choice, of course.
Workaround
Only works for slides. For slide notes and other layouts I do not have a solution. Also, in many cases it is less work to just make a copy where you delete the undesirable elements before pdf export. That is, unless you start thinking like me, that Draw is a sensible presentation tool … 
- Save your presentation as a drawing (odg)
- Open the drawing file in Draw.
- Add a layer (you could call it “NoPrint”). Set it to visible but not printing.
- Click and hold the objects you don’t want to print for a second or so, and the pointer changes to “special drag mode” where you can drag it to a different layer. Just drag it to the NoPrint tab and drop it there.
- When you are done with your objects, shift+click the NoPrint to toggle the Visible property, to verify that all objects are in place. Shift+click again to make the objects visible.
- Make your export.
Do note that visible and printing are independent properties. You can have visible objects which don’t print, and objects invisible on screen which show when printing. Not as powerful as the css @media rules (or your mentioned LaTeX solution which I do not know yet), but for some cases it may help you.
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