Did you perhaps previously have GarageBand '11 installed on your Mac at home? Or any Jam Packs? Loops installed by older versions will be available in GarageBand 10, but if you install only GarageBand 10 from scratch and not on top of an older version, the older loops and instruments from the previous versions will be missing.
Or do you have at home also MainStage or Logic installed? There may also be loops from Soundtrack Pro, that can be used by GarageBand.
You can simply copy the loop library from your Mac at home to your new Mac and then rebuild the loop index in GarageBand.
The loops are installed in the folder /Library/Audio/Apple Loops/
Copy any missing loops you want to add on the Mac at work to the corresponding folder to install them.
Then open the Loop Browser in GarageBand, open the menu "Loops" at the top of the Loop Browser and select the last item - reindex all Loops.
Check, if the GarageBand Preference "Loops: Keyword browsing: Filter for more relevant content" has been enabled on your Work Mac. With this option active, you will only see a small subset of your loops, so disable it.