What you described is expected in GNOME 3, that's how it's supposed to work. You're probably looking for a more traditional application menu akin to other desktop environments and other operating systems.
You can get an application menu using various GNOME Shell extensions (refer to this know more about extensions: How do I install and manage GNOME Shell extensions?), for example:
- Application Menu
Add a category-based menu for applications.

- Frippery Applications Menu
Replace Activities button with an Applications menu

Gno-Menu
Gno-Menu is a traditional styled full featured Gnome-Shell apps menu, that aims to offer all the essentials in a simple uncluttered intuitive interface.

Note that Gno-Menu is a fancier alternative, it provides many more customisations, but it might have some stability issues.
Note: You can also remove the 'Show Applications' button altogether by running the following command in Terminal:
gsettings set org.gnome.shell.extensions.dash-to-dock show-show-apps-button false