I don’t think there’s a single, standardized approach naming for this work, but this is how I think of these two documents:
Inventory: An inventory is just what it sounds like–an itemized list of all the content that exists (including offline content, if that’s appropriate). There is a level of analysis here, as characteristics of the content, such as target audience, date of publication, topics, and other criteria specific to the project are outlined. These are simple, straightforward documents, with a primary focus on seeing what’s there, contentwise, and tossing it into the appropriate conceptual pile.
Audit: The audit is a more analytical exercise, in my opinion. It’s an inventory, yes, but with a level of editorial/storytelling detail that isn’t usually in an inventory. For instance, in an audit, I provide more detailed notes–highlighting themes noted in the content that may not have been discussed yet in the project and spotlighting key insights on the style of the content and its presentation.
I love audits because they’re where interesting possibilities can come to light. The output might be something shared with creatives, like: “The copy makes a really big deal about the texture of their fabric. I feel like there might be something to work with there.” It can also be a gut check for the account/business analysts, if the insight’s something like “They say they’re all about the human touch–but I don’t see anything about that on the site. Is the client aware of how big a shift the focus on ‘human touch’ is going to be?” It might be a heads-up for the IA, along the lines of–”Their product lines are really, really dense and confusing. Search/navigation is going to be a tough nut to crack.”
I’ve seen these terms defined differently, and I don’t actually care what the documentation is called, as long as the entire team is aware of the differences and specific about what they’re asking for.
But I would like to note that neither of these documents is a simple list of URLs. I’ve seen, more than once, content projects where the strategist has been told he can skip the audit stage because the client has already done that, only to be provided a matrix of web addresses completely absent any other details–documentation that’s helpful, but not what a content strategist needs to do his work.