If testing to IEC61010 (which as it is a multi-meter it should be) the surge test for the 1000V CATIII is the same as 600V CATIV. Generally, a manufacturer will quote the CAT IV rating as it "looks better" on the documentation. Quite often you will see both ratings marked on the instrument and documentation. As a for instance, look
here. Fluke have rated this as 1kV CAT II, 600V CATIII. What this means when you look at it is that in CAT II situations you can use the voltmeter up to 1kV, but in CATIII situations you should de-rate it to 600V. Similar argument for the BM857.
My big question is why they would only quote the CATIII rating might be so they can say "our new range of 1000V meters" but that is only a guess.
The one thing that does grab my attention on the datasheet I have just found was that it said "CATIII 1kV AC/DC" CAT ratings are always AC.
Short answer - they are not the same but they are equivalent.
The Wikipedia Article seems to provide a few more specific figures as far as max current/power and what type of external protection measures are in place, though your best bet if you're really concerned about what CAT rating you should get for different situations would be the IEC 61010-20-030 standard (unfortunately not free).
The NI document sums it up pretty well. The explanation in 61010 of the CAT situations isn't much more detailed.
Neil