I've only recently begun working in the quantitative finance field, and I've noticed that some time series I'm given are labeled "seasonally adjusted", and some labeled with "seasonally adjusted annual rate". What's the difference between these two data transforms?
Seasonal adjustments per se are a topic in and by itself, see for example this Wikipedia page.
As for the added "AR", imagine an event with an unconditional average of '100' (to pick a base) when measure monthly. So the annual average is 1200, and similarly, a 'SAAR' series accounts for both recurring seasonal patterns (quarterly, monthly, weekly, daily, intra-daily, ...) and also scales the measurements to an annual total.
This wasn't really a quant finance question, maybe try the Stats sister site next time around.
A SAAR series is expressed as if period-over-period growth were to occur for an entire year. Real GDP is reported this way. A report of 3% GDP growth in a quarter does not mean GDP grew 3% in that quarter. It means GDP would be 3% higher in one year if this quarter's growth were to occur over 4 consecutive quarters.