its thick or thin, a thick client contains both user interface and business logic. A thin client contains user interface and coding to communicate with a piece of software which holds the business logic.
Thick clients occur in 2-tier application design, mostly together with a database back-end
Thin clients occur in a 3-tier application design, for example MTS for the middle tier, database for the back-end and a thin client for the user to communiate with the MTS component
Serverside Web applications can be an example of a 3 tier application design. The presentation part in the browser (thin client), the business logic (the serverside code, maybe communicating with a dll) and the database (f.e. SQL server)