Apple Users

So long as the device is already paired it is friends with the computer and they'll hook up regularly, "discoverability" is a completely separate function - and usually has to be activated and turns itself off after a minute or so. It's like temporarily turning on a lighthouse beacon so the ship can find its way in, then turning it off when once it's docked - the dock is still open, just not as easy to find.

It is similar to broadcasting your SSID network name on WiFi or not. You have to change this manually. It's a bit harder for average people to find your network if you don't broadcast the SSID name for them and they have to know the exact name to type in to connect.