so to wrap it up, closed circuit is required for steady current, regardless if it's AC or DC. For momentary one-time current, static or DC, the current only need a difference of potential between 2 points
is this right?

 

Current always needs a complete circuit to flow, but you must be aware (know more about electrical science than simple circuits) of how the loop is being closed.

Is this a 'closed circuit'?

Topologically, there is a gap in the circuit.

But, there is current flow in the circuit.

 

this is not the case with static current or any DC current.. they just need two points of different potential to flow.. not any closed circuit.

Not so.
You can have a voltage difference between to points but current will not flow unless there is a complete return path for the current.
Otherwise where would the current go?

 

so to wrap it up, closed circuit is required for steady current, regardless if it's AC or DC. For momentary one-time current, static or DC, the current only need a difference of potential between 2 points
is this right?

Yes and no. When you bring a charged object near another object, the electric fields will cause charge to redistribute on the object until they are in equilibrium. This is a current flow, albeit it very tiny and very transient. If you move the charged object back and forth, would will induce a corresponding current flow back and forth in the other object. These kinds of miniscule current flows happen all the time. They happen in the drywall through which electrical wiring passes, for instance. But the scale is such that we can completely neglect them (in all but the most sensitive of scenarios).

But saying that the current ONLY needs a difference of potential between two points is going way to far -- even after any miniscule current has died, there is still a difference of potential between the two points with no further current flowing.

 

Is this a 'closed circuit'?

that's a perfect steady AC closed circuit.. each terminal of the capacitor is connected to a different terminal of the AC source

But saying that the current ONLY needs a difference of potential between two points is going way to far -- even after any miniscule current has died, there is still a difference of potential between the two points with no further current flowing

thanks for the response.. I forgot to mention a conductor between those two points of different potential