I have a lot of customers who are really confused by the two Microsoft FAST products. First we have Microsoft FAST Search for SharePoint. The core search engine of this product is a port of the original FAST ESP 5.3 code base. There were very few features added, mostly it was a project of remediation. The search engine was ported to 64bit, and put through all of Microsoft's strict code review tools and security screens. Finally, Microsoft would not allow any open source code to be shipped, so a few major components were written from scratch. The biggest one of these was the replacement of CORBA.
Much of what is seen as new is the integration with SharePoint. There are new FAST administration screens that manage the FAST fields (called managed properties) as well as two new SSA components to handle the FAST queries and crawling. In addition, a complete PowerShell administration layer has been added both on the SharePoint server as well as the FAST server. For those familiar with FAST ESP, you will notice most of the old command-line administration tools are still there.
Microsoft FSIS (FAST Search for Internet Sites) is an attempt for Microsoft/FAST to get rid of the aged python document pipeline stages as well as the query result processors. FSIS is a complete server FARM that exists separate from ESP. It's job in life is to process content before it is sent to ESP for indexing as well as process queries. It's framework allows you to do some complex tasks the least of which is query federation. The most powerful feature I have experienced is the ability to cleanse the content before it is sent to FAST ESP.
FSIS comes with a Visual Studio plugin to graphically create query and document processing "flows". These flows can be created and run from within the development environment. It also comes with the IMS toolkit which is a JavaScript API for querying against FSIS.
While FSIS has some good ideas, it falls short in many areas. First it requires its own farm which increases the cost of ownership significantly. Second, the only method to query is via the JavaScript API. I guess you could perform calls directly to the WDM (Web Delivery Module), but that interface is not well documented. Finally, the documentation and web support is very minimal. The lack of noise on this product makes me wonder if Microsoft is serious about its future.
While FAST Search for SharePoint is a solid product, FSIS appears to have been shipped too soon. There are a lot of rough edges and crashes quite frequently. Further, if you plan on using FSIS with SharePoint, don't bother. It doesn't work. If you install the FSIS WDM under SharePoint it will crash on first call. Also, the JavaScript toolkit won't run under SharePoint and neither will the web controls. That being said, there are good reasons to use FSIS behind SharePoint. For one of my clients we wrote a complete IMS.NET API that replaced the JavaScript API. We also re-wrote the FSIS WDM so it would work under SharePoint. So there are options, just not OTB options.