Meaning of "bars" icon in System Tray

I recently replaced an old Windows 7 desktop with a new more powerful Windows 7 desktop. My old machine was wired to a Gigabit Ethernet router, and so is the new one. Here's the difference: The new machine has wireless adapter, and when I look in the Notification Area, I see a "bars" icon. On the old machine, which did not have wireless, I saw a "wired connection" icon in the Notification Area. See attached screenshot.

When I first saw the "bars" icon, I thought the new machine was actually using the WiFi connection, rather than the (much faster) wired connection. But after poking around, I was convinced that traffic was going over the wire.

I would definitely prefer to see the "wired connection" icon in the Notification Area when the machine is using it. But when I choose "Customize" I do not see the icon. The "bars" icon is simply called "Network." I find that confusing. What happened to the wired icon?

Or as I do if not wanting a Desktop to use the Wireless/Wi-Fi, disable the Wireless in Device Manager and/or Networking. It may also be possible to disable the adapter in the BIOS then Windows shouldn't see it.

If properly set up a Wireless Router should require entering a password/passphrase/pass code for a connection to be established using Wi-Fi. I have seen issues when there was also a Wi-Fi-capable printer in use.

Why would Windows choose to use a Wireless connection when a much faster wired connection is available? And why would the traffic volume on the wired network be so high if it were using wireless (see attachment)?

I should have mentioned that, before posting here, I followed instructions I found elsewhere to tell Windows to prefer the wired connection:

Control Panel -> Network and Sharing Center -> Change adapter settings
Press Alt key to get the menu bar (menu bar is not shown otherwise)
Choose Advanced -> Advanced Settings.
Re-order your connections in that list.

I did this and moved "Local Area Connection" to the top (see attachment). But I still get the "bars" icon.

I will disable the wireless as some of you suggested, but I find it hard to believe that this step would be necessary.

I have restarted many times. As suggested, I disabled the wireless adapter and now I see the "wired" icon in the Notification Area. Odd indeed!