Indeed, both the thin client and the thick client can work with applied solutions running in managed application mode. And both clients can work directly with file infobases and connect to a 1C:Enterprise 8 server cluster over LAN or TCP/IP.
But they do have different capabilities in how they connect to infobases. The thin client provides connection to infobases using HTTP and HTTPS protocols through a web server. In other words, a thin client can connect users who are working online, over the Internet.
In comparison to the thick client, the thin client requires less hardware resources and is provided as a separate, smaller distribution kit. This small distribution kit can be transferred to a remote user, then he or she can install it independently and connect to the infobase.
The thin client supports regular user work scenarios.
The thick client is intended mostly for administrators and developers to work in Designer mode (where they can perform administrative actions or modify the applied solution).
You might also need the thick client for backward compatibility with applied solutions created in earlier platform versions. This is the case if an application has not been adjusted for use in managed application mode or has been adjusted only partially, which requires the use of both ordinary and managed forms.