What is the difference between implicit type conversion and explicit type conversion?

Is it true that if two objects return True for is operator, they will also return True for == operator?

Two objects (say a and b) when compared using == ,return True. But Python gives False when compared using is operator. Why? (i.e., a == b is True but why is a is b False?)

Are these values equal? Why/why not?

1. 20 and 20.0
2. 20 and int(20)
3. str(20) and str(20.0)
4. 'a' and "a"