I expected that these would be the same thing, but after looking around the Appcelerator website, it seems that they may actually be two separate IDEs.
Currently on the site (http://www.appcelerator.com/), under the Products menu item are links to Appcelerator Platform and Titanium. The latter is obviously the IDE and the former is just the name of the complete package that includes the dashboard, analytics, marketplace and all that other stuff. It is not an actual piece of software.
Note also that only the Titanium page has breadcrumbs showing the other products.
However, after Googling "appcelerator studio", the second result was a link to this page: http://www.appcelerator.com/platform/appcelerator-studio/
At first I thought it was a disabled link that was cached in Google's index, as I couldn't find any internal link on the site to this page, but then I read the following line:
Appcelerator Studio IDE – a powerful Eclipse-based IDE, based on Titanium Studio IDE
So I was confused; is Appcelerator Studio a new IDE that they haven't made public yet?
No. Its the enterprise edition of their platform.
It includes:
Built-in profiler, code analyzer, and LiveView editor to accelerate prototyping and development and measure code quality.
All features not available in the community edition.