Which is more user friendly for the "mass population" on the internet? Is it better to present the traditional "category" pattern when having them post something on your site, or is the "tagging" pattern considered user friendly enough to rely on?
Well they should be for different uses. Tagging is for adding some meta data to an object. To describe it. Categories are more organizational and a way of grouping all content into few groups.
Here is a good article explaining the difference.
So its the age old answer that "it depends" on the use. If you want the users to just add more description and meaning to images, posts, and other objects, then go with tagging.
If you want them putting those into few buckets that summarize all the content into topics, than categories.
As a UX professional, I'm not convinced there really is a difference.
The article jonshariat links to makes a case for categories being mutually exclusive. If universally true, then that's perhaps the one difference, but given that many sites use tags as a form of category browser, I don't think that holds true either.
But let's assume it does. From an end-user navigation POV, the difference is then whether or not your 'buckets' are meant to be mutually exclusive of not. So, perhaps that's the question you need to ask...for the particular needs of your users of your site, should the data be put into mutually exclusive buckets, shared across buckets, or both?
As for 'understanding' that, well, that's up to how you design the UI to navigate the structure.
Categories evolved into tagging when they started appearing a little superfluous for light classification schemes. Tag(as called) play a significant role when target information is either too much or too heterogeneous to enforce a comfortable classification. It's a great way to improve findability without getting too much in the way a user experiences a system or consumes an information..if designed conventionally! :)
UX majorly and mostly dictated this distinction from its very inception.