Answer 1

Every time you define an object in python you are creating new object with new identity, check this:
class Ob:
pass
a = Ob()
b = Ob()
>>> a is b
False
But python has special case with integers smaller than 256, it caches (integer objects) in range (-5, 256) for perfomane reasons, look at this:
a = 5
b = 5
>>> a is b
True
a = 10
b = 5
>>> a is b*2
True
a = 500
b = 250
>>> a is b*2
False
Id varies with strings that has a length higher than 20 charecter:
a = "xxxx"
>>> a is "x"*4
True
a = "xxxx"*5
>>> a is "x"*20
True
a = "xxxxx"*5
>>> a is "x"*25
False
In your case the variable "a" is an (input object) and "b" is another (input object) that has new identity, so id of variable "a" != id of variable "b",
But one byte of the input has special case?
a = input("")
b = input("")
>>> a = "x"
>>> b = "x"
>>> a is b
True
>>> a = "xx"
>>> b = "xx"
>>> a is b
False!

Answer 2

it doesn't vary if they're the same.