Question

which are the same when referencing for 1 and 2

1) ideal = exact

or

ideal = approximate

2) theoretical = exact

or

theoretical = approximate

explain....!

Answer 1

In general, ideal means there are no losses or noise or any unwanted parameters involved.

Theoretical means an analysis made of a particular concept with all the known parameters taken into consideration.

For example, for an operational amplifier operating in open loop,

ideally the gain will be infinity (i.e. the output voltage will reach infinity)

but theoretically the output voltage will reach the supply voltage

However, practically the output voltage may not even reach the supply voltage due to any internal losses

So essentially, theoretical value can be viewed as an approximate value that can be achieved using a particular concept, whereas an ideal value may not be interpreted as an exact value or approximate value. It only means that the value can be achieved when there are no real world losses etc. at the play.