There are iOS apps that allow you to log into a Mac on the same WiFi network. They display the Mac screen on your iPhone or iPad, and provide a keyboard to log in. Finger can be used as mouse; tap to click.
The Mac must have "Screen Sharing" turned on. I use a free one called "VNC Viewer" and it's worked well for me -- I like it. There are others on the Apps store -- look for "VNC" or "Screen Sharing". Hope I understood your question correctly!
No. There is no need for any additional server software on the Mac, because macOS has a VNC screen sharing server capability built-in. All you need to do on the Mac is go to System Preferences-->Sharing-->Screen Sharing and check the box to turn the feature on. While you're there note the "Computer Name" of your Mac.As far as I understand it needs both, an app on my phone / iPad as well as their server software on the mac?