St. Louis City is entirely independent from the surrounding St. Louis County and covers an exceptionally small area by the standards of most big cities (~66 sq/mi). Some similar cities have addressed this by merging with their surrounding county (Indianapolis, for example, which is about 368 sq/mi), but even those that haven't (e.g. Kansas City) still cover a much larger portion of their region (316 sq/mi for KC).
It's very easy to exit the city-proper in St. Louis and not feel at all as though you've left the core of the city. The inner-ring suburbs are quite urban and, while the distinction between them and the City itself is the source of much local posturing, it's a misleading delineation if you're trying to figure out just how big St. Louis really is.
(As a side note, this way of dividing up the region also has a significant effect on the City's infamous crime statistics, for reasons that should be pretty obvious with a little bit of thought. That is to say, if you define almost any city as only its most inner core, then you're going to end up with much higher crime rates than if you include its suburbs. And if you're comparing one city that doesn't include its suburbs with cities that predominantly do, then, well, you get the idea.)
In other words, the larger MSA/CSA numbers more accurately reflect the relative size of both St. Louis's urban core and the surrounding region.