Some openers have separate remotes. But they are fairly old.

The ones that I think of have the receivers in the wall mounted manual opener.

If your opener has a short wire sticking out of then the receiver is built in and in most cases replaced with the controller board.

If you get the model number you can enter this chart and see what logic board it takes.

http://www.aaaremotes.com/liftmastercompatibilitychart.html

But you can also get separate receivers and reciever/remote packages.

Here are two from Liftmaster/Chamberlain the makers of Sears Openers.

http://www.aaaremotes.com/liungadooppl.html

http://www.aaaremotes.com/secrlichgado2.html

You get packages with multiple remotes and remotes with multiple buttons if you want to replace update both units.

http://www.aaaremotes.com/reloboandexr.html

You can also get keypad remotes and other accesories.

I believe that Sears also sells a remote/receiver upgrade package.

AAA Remotes also has generic units from other manufactures.

If you want to it to work with the existing Clicker and/or match the other unit or get compatable parts contact AAA REmotes about what you need.

Disclaimer I have no relatingship with AAA REmotes (not even bought from them) but I have found that their website is very informative.