This seems like a stupid question, but the closest answer I could find in the sitecore docs I have (online and offline), is that shared fields are “shared across languages”. I took that to mean a shared field’s content would be the same across all translations of that item in sitecore.
Is that correct?
Yes, that’s correct – the same across versions and languages of an item. Here the quote about Shared from SDN (though for 5.3, still valid for 6.x):
And I can foresee your next question: if both Shared and Unversioned are checked, the field is Shared. You can read more about how it is stored internally here on my blog.
Hope this helps.