The computing term "Thin Client" arose during the 1990s, when it referred to a mythical "network computer" that had no disk drive, to be used in a configuration where the bulk of the processing took place on the server. The idea was that we would all have cheap, slinky "net computers" that accessed online services, while we rode hoverbikes and spent weekends on the Moon. In practice few were built and none were sold, probably because they seemed to cost about as much as regular computers, networks were slow and unreliable, there were no office applications available and people liked having their own stuff.
Later, with the growth of the Web, a new "thin client" model arose, and nowadays the term has come to mean an application that you use through your web browser.
The opposite of a thin client is the configuration where a big old application has to be installed on each machine, and this naturally became known as a "fat client".
The problem is that in management circles, you can't say the word "Fat". "Downsizing", certainly. "Leveraging", of course. "De-scoping", "White Box", "Blue Sky" and "Results-driven goal-oriented win-win synergies", no problem, but you can't stand up at the weekly Heads Of Department meeting and say "Fat", and so we started to hear the term "thick client". Well, it's the opposite of thin, right?
Well, no. The entire point of "thin client" is that it's slimmed down, not anything to do with its depth. It's skinny. It's light. It's lo-cal. It's slender, svelte, lean, trim and nimble. It has not, in short, eaten all the pies. The opposite of that is not "thick". In any case, as a good friend (who it must be said, likes her pies) remarked, what about people who are a bit thick? How must they feel?
The configuration in which a big old application has to be installed on each machine is called "fat client". Get used to it. Or, if human life is directly at risk, "rich client". Or if you must, "smart client". But let's leave those thickies out of it.