Since I am not a techie, I'll try to give you my layman explanation re tags and categories.
The categories still exist (even if the DB tables have been renamed) and yes, they are exactly for that: grouping relevant posts together. Therefore, I think a site should have a minimum necessary number of categories... otherwise having 200 categories for 250 posts - makes the whole idea useless.
However, tags, on the other hand, are different. Think of them as "labels" or tags as in "red tags" (when retailers have big sales). Not meta tags in any case! They serve for a different kind of 'taxonomy' or grouping.
E.g. I can have one category named "Languages" and everything I write and is language related should go there. Now, let's say I'd like to offer my visitors (and certain aggregator site, like Technorati etc.) to find posts not only by the general category Langauges but also posts that are "tagged" with, say, Tagalog or Russian. So, I tag them like that. I do NOT want a category for every language because there are 6,912 known living languages :)
Now, the interesting thing is that I can use tags "across categories" so to speak. So, I can have 2 posts in my Languages category tagged with "Russian", and another post in Roulette category, also tagged with "Russian" (because I wrote there about Russian roulette.
So, when clicking on the "Russian" tag - it will bring you up all the 3 posts with that tag.
Does it help?