Not everyone call it this, but a lot of people do. The name probably arose from the sound that the buttons make when you press them or the noise produced when you changed channel.
They both use an "RF" control, something similar to an SOS signal on a boat.
I'd say its still called a television! Televisions came out for a long time without remotes. Now you can get universal remotes to suit all TVs.
eBay or an RC store
The ORIGINAL Idiot Box!