user539 You connect the Pixel 8 to a monitor that supports USB-C DP Alternate mode using a USB-C cable that also supports DP Alternate mode. If the monitor doesn't support USB-C DP Alt mode you can connect the Pixel to a USB-C hub or adapter that supports it, and connect to the monitor through the adapter with an HDMI or DP cable.
You can find more info on DP Alt mode on the web, such as here: https://www.benq.com/en-us/knowledge-center/knowledge/usb-c-introduction-what-is-dp-alt-mode.html
When you connect the Pixel 8 to the monitor, the phone will ask you if you want to mirror the screen. That feature is commonly called "screen mirroring" because it, well, just mirrors the screen – it does nothing but mirror the phone's screen. That includes keeping the aspect ratio of the phone screen, so it won't fill up the monitor (unless you happen to have a monitor with the same aspect ratio as your phone). No additional features that let you adapt your workflow to a bigger screen.
What is commonly called "desktop mode" in this forum is a feature hidden behind toggles in developer options. It's far different from screen mirroring because it attempts to adapt the UI on the monitor to a workflow that works better for usage with a keyboard and mouse without having to interact with the phone. Basically an attempt at a desktop OS interface. I say attempt because, in my personal opinion, it is currently far, far away from being a usable alternative to any desktop OS environment: it's riddled with tons of bugs and has far less features than you'd expect from a desktop environment.
user539 Let's say I have pixel 8 as a daily.
If you're contemplating buying a Pixel 8 or newer just to have desktop mode, my personal opinion is that, currently, that is a waste of money. I think you'll highly likely be disappointed. I haven't tried desktop mode with Android 16 QPR1, but from reading the GrapheneOS Alpha/Beta Testing channel in the chat rooms it looks like people are saying it hasn't improved.
If all you need is screen mirroring, though, then yes, screen mirroring works well if you simply want to mirror the screen.