So I create an ad hoc network every now and then on my Mac for various reasons, and I have found lately that when I click on the Wi-Fi icon in the Mac menu bar, even when the network is not on, it still shows up under "devices" as a valid network. How do I actually shut off my network?
What many Wi-Fi products refer to as an "ad hoc" network is what the 802.11 spec refers to as an IBSS. It's important to note that the originator of an IBSS does not control it at all. Once one or more additional devices join the IBSS, all devices in the IBSS are completely equal peers, and they all participate in maintaining the network, even after other members leave. Because the originator is not special, the originator can leave the IBSS it created and all the other peers in the network will continue to maintain the network until you turn them all off or tell them all to join other networks or whatnot. If you've ever seen the "Free Public WiFi" IBSS while waiting in an airport terminal, you already know about this. :-)
So if you created an IBSS on your Mac, joined it from, say, your iPad, and then left the IBSS from your Mac, your iPad could still be maintaining the network. Turn off Wi-Fi on the iPad or have the iPad join another network if you want the IBSS to go away.
You can always look at disabling the aircard by turning it off and cleaning out existing ad hoc profiles.
System preferences -> network -> aircard (or what you have labled your wireless connection). NOTE: Do not delete your aircard profile.
Profiles: aircard -> advanced and then delete by using the '-' sign at the bottom of the list.