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If what I heard is true you'd be surprised if you did! Apparently the nominal cross section is defined based on copper with a certian specific resistance. If copper with a lower resistance is used, the actual wire size can be smaller than the nominal cross section!

It is clear that the NEC table doesn't show actual trade sizes, I'd consider it a tool for easier comparison. However, it'd be much more useful if it used the cumulative area of strands in case of stranded wire since that's what you want in an ampacity table.

I guess the main use of said table would be something along the lines of "Ok, I've got NEC tables, I am working to US specifications but have to use metric wire. What size conductors do I need to use?".

For those interested: this PDF shows what such an ampacity table usually looks like in Europe (page 4)
http://library.abb.com/GLOBAL/SCOT/SCOT209.nsf/VerityDisplay/C6ED3B4782C5F804C12572A5003A1CA0/$File/2CDC401002D0102.pdf

Page 5 shows maximum ampacities under specific conditions and associated standard sizes of OCPDs.

You folks talk funny

I think I was able to sort it out.

Nennquerschnit = wire size
Kabeln = Cables
Anzahl der gleichzeitig belasteten Adern = number of conductors
Strombelastbarkeit = amp rating
Nennstrom = Ampacity

Am I close?

You nailed it pretty close!
It's current-carrying conductors though, so if planning a 2w 1ph circuit it's 2, in case of 3ph 4w it's only 3.
Nennstrom is the nominal breaker/fuse rating and Strombelastbarkeit is the wire ampacity.

Cold-drawn metal of any description will probably be right on the bottom limit of the spec., on instructions from the bean counters. Pull a few miles of wire through a die and 0.002" on diameter adds up to a heap of $$$, especially where copper is concerned.