Gah! You're right. Austria is not Germany. What's the difference between the two anyway?
It's a bit like asking, what is the difference between the USA and Canada
...or how do you sum up 800 years of history in a few lines? Short version, Austria is a country and has been for very long time. Germany is an amalgam of a bunch of other germanic countries (Austria excluded), which lives together in an empire/federation (and is only a few centuries old). Otto von Bismark is often credited with leading the unification wars. After Prussia and Austria had conquered most other german speaking nations as "allies", they went to war against each other over the spoils. Prussia won out in the end and a united "Germany" was the result.
I am sure Morgoth can add more details/correcting my mistakes. Austria had for many centuries close ties to Spain and The Netherlands/Burgundy through family ties (the Habsburgs).