What is Photoshop Standard?
The Standard version of Photoshop includes all of the tools that you know and love and traditionally associate with the application. More information here: Image editor software
What is Photoshop Extended?
Starting with CS3, additional specialist tools were added to an Extended version of Photoshop. This included 3D and analytic tools. More information here: 3D design
What are the real differences?
A high level comparison can be viewed here: Adobe Photoshop family – Comparison guide
A more detailed look at the features within each version can be viewed here:
Additionally, if you see a topic in Help that says "(Photoshop Extended)" in the title, this feature is for the Extended version only. This search will show these Help articles: "(Photoshop Extended)"