When clicking "Applications" on the top-left in Fedora the overview screen appears.
However in CentOS this opens a Windows-like start menu.
Is there any way to make this open the overview screen instead?
The reason why Gnome behave differently in Centos compared to Fedora is because Centos uses Gnome classic and Fedora use the "regular" gnome as default.
To get the "overview screen" instead, you just have to logout and select "Gnome" instead of "Gnome classic", see figure below.