Remote Desktop Connection works via WiFi, but not via ethernet

I have a desktop and a laptop.

The desktop is connected to the internet using an ethernet cable.

When the laptop is connected using WiFi, I am able to make an RDC connection to it from my desktop.

When the laptop is connected using an ethernet cable, I am NOT able to make an RDC connection to it from my desktop. It gives the following error:

"Remote Desktop can’t connect to the remote computer for one of these reasons:

1) Remote access to the server is not enabled
2) The remote computer is turned off
3) The remote computer is not available on the network

Make sure the remote computer is turned on and connected to the network, and that remote access is enabled."

I know the laptop is on the network because it appears under my network list in Windows Explorer, on my desktop and on my laptop.

What can I do to make an RDC connection to the laptop when it's connected via ethernet?

There are two different network profiles on your laptop, one for wifi and one for Ethernet. Check the differences between the two. There has to be a setting that is wrong in your Ethernet protocol.

Thanks. Do you know where I would go to check that?

I looked under Network & Sharing Center, then under Advanced Sharing Settings, and it lists 3 different network profiles - Home/Work, Public, and Domain. But I can't find anything that applies to wifi versus ethernet.

Network & Sharing Center / Change Adapter Settings. Your two adapters will be listed here. Right-click and choose Properties on each one to see the settings.

I appreciate your help. I'm still stuck on this though so you'll have to excuse my ignorance.

As far as I can tell, all settings are the same. I've attached screenshots.

I also tried going into the Sharing tab and changing the option in the Home Networking Connection box, but it doesn't seem to save. I press OK after changing it, but when I go back in again, it's back on "Select a private network connection".

Sorry, I don't have an answer for this one.

I was able to get it to work by using the machine's IP address instead of its name. Any idea what that means? Is that an indication that something is not set up properly?

The IP address is one way to specifically identify a computer. The name is another. I'm not sure why one works and the other doesn't; my guess is that, for RDC, the IP address is a better way than the computer name.