At the start of some television shows and movies, they show a countdown type thing that looks kind of like a radar chart with numbers in the middle. Does it have a special name or is it just a countdown?

I saw a whole site of them last week and spent an hour looking last night with no success. There are a few different timers you refer to. The one I saw is the electronic clapperboard the studio sees but we don't unless they make a mistake. They had all on from the old manual ones to the computer generated, though they all look similar.
The second is the ones used in programme intervals which are just countdown timers or clocks see lower part of page
I haven't seen any others you describe so maybe they are the accidental clapperboards that sometimes sneak in for a few seconds before they change cameras. If I find the page I'll add it.