Can I set up my Helpdesk in a way where different clients see different articles?

Yes, you can set up custom visibility rules so that different clients see different articles.

1. Make sure that your articles are assigned one or more tags. 
2. On the table of contents on the right sidebar you will see a list of your tags. For the tag for which you want to set up custom visibility, click the action button (...) and then click Visibility. Note that the visibility rules you are setting up apply to all articles associated with the tag.
3. On the visibility settings modal, select Custom visibility. You can set up custom visibility by selecting specific clients directly, specific companies (all associated clients will be included), or custom fields (clients who have the specified custom fields will be included).