Throwing wheel is the wheel named after the thing it does. Throwing is shaping clay by hand on a rotating head, and a throwing wheel is any machine that turns the head with enough torque to let you do that against real resistance.
What throwing asks of the machine
Centring puts the highest load on a wheel: the potter presses down and inward with their whole upper body against a spinning lump. The machine has to hold speed against that, which is why stated centring capacity is the specification to compare. Pulling a wall is gentler; trimming is gentler still but needs fine control at low speed.
Why beginners blame themselves
On an underpowered wheel, the clay wobbles because the machine is slowing rather than because the hands are wrong, and the beginner has no way to tell the difference. That is the strongest practical argument for buying a wheel with capacity to spare: it makes every failure informative.
Bats and removing what you threw
A pot thrown directly on the head has to be cut off and lifted, which is where wide or thin-walled pieces are lost. A bat, a removable disc that pins or sticks to the head, lets the pot be lifted away untouched. Any wheel used for anything other than mugs benefits enormously, so check what bat system a machine takes.
Where to throw
Somewhere with a socket, a floor that can be mopped and room for a bucket. Throwing is wet work and slip goes everywhere, which is the argument for a splash pan and against a wheel in a carpeted room. Keep the slop bucket for reclaim rather than the sink, because clay settles in traps and blocks them.
Questions people ask about throwing wheel
What is a throwing wheel?
A potter's wheel, named for throwing, which is shaping clay by hand on the rotating head.
Why does my clay wobble?
Either your centring or a wheel slowing under load. A machine with capacity to spare removes the ambiguity.
Do I need bats?
For anything wide or thin walled, yes. They let a pot be lifted off without touching it, which is where wide pieces are usually lost.