I don't know what the web farm is but the other 2 are different products though related.
CR Advanced Developer is the most featured edition of Crystal Reports. Crystal Reports is a reporting tool allowing you to develop reports on data from many different databases. In the past there were different licensing "level" or editions.
CR Standard was the basic edition which allowed a user to develop reports for his own use and on his machine. Limited database types and limited export capability. Was not licensed for use with an application.
CR Professional Next step up. Increased capability mainly more databases and export formats. COuld be used with applications but only for inhouse use non-web use.
CR Developer - Full capability with a license to build applications for use in house or delivery to customers as aclient application
CR Advanced - Full capability and it included a copy of CR Server.
Feture comparison by version and edition
http://www.businessobjects.com/global/pdf/products/crystalreports/crxi_feat_ver_ed.pdfCrystal Reports 10 Enterprise - A tool to enable a company to provide company wide access to reports without building its own application. Reports are loaded into Enterprise and can be scheduled ro run manually. It also provided some secutiry so only users with permissions could run some reports.
I hope that helps
mlmcc