When you choose a project in the running Client and do an "update" this updates the project settings, i.e. communicates finished Results and updates your general and project preferences from your settings at this project server.
To update the Client itself, terminate the BOINC Client (usually "Exit"), then download the new client version from the BOINC page (there should be a link named "download" on the front page of every project) and install the new Client. In rare cases (i.e. previously using old clients like 4.09) you will need to uninstall the older Client first, which btw. means you'll lose alt the work in progress.
BM

update boinc-client
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> In rare cases (i.e. previously using old clients like 4.09) you will
> need to uninstall the older Client first, which btw. means you'll lose alt the
> work in progress.
Actually it's pretty good at keeping the work in progress around even when you uninstall the code and install another version.
- Rusty McGee Johnson