Is there a difference between "==" and "is"?

There is a simple rule of thumb to tell you when to use == or is.

• == is for value equality. Use it when you would like to know if two objects have the same value.
• is is for reference equality. Use it when you would like to know if two references refer to the same object.

In general, when you are comparing something to a simple type, you are usually checking for value equality, so you should use ==. For example, the intention of your example is probably to check whether x has a value equal to 2 (==), not whether x is literally referring to the same object as 2.

---

Something else to note: because of the way the CPython reference implementation works, you'll get unexpected and inconsistent results if you mistakenly use is to compare for reference equality on integers:

>>> a = 500
>>> b = 500
>>> a == b
True
>>> a is b
False

That's pretty much what we expected: a and b have the same value, but are distinct entities. But what about this?

>>> c = 200
>>> d = 200
>>> c == d
True
>>> c is d
True

This is inconsistent with the earlier result. What's going on here? It turns out the reference implementation of Python caches integer objects in the range -5..256 as singleton instances for performance reasons. Here's an example demonstrating this:

>>> for i in range(250, 260): a = i; print "%i: %s" % (i, a is int(str(i)));
... 
250: True
251: True
252: True
253: True
254: True
255: True
256: True
257: False
258: False
259: False

This is another obvious reason not to use is: the behavior is left up to implementations when you're erroneously using it for value equality.

is will return True if two variables point to the same object (in memory), == if the objects referred to by the variables are equal.

>>> a = [1, 2, 3]
>>> b = a
>>> b is a 
True
>>> b == a
True

# Make a new copy of list `a` via the slice operator, 
# and assign it to variable `b`
>>> b = a[:] 
>>> b is a
False
>>> b == a
True

In your case, the second test only works because Python caches small integer objects, which is an implementation detail. For larger integers, this does not work:

>>> 1000 is 10**3
False
>>> 1000 == 10**3
True

The same holds true for string literals:

>>> "a" is "a"
True
>>> "aa" is "a" * 2
True
>>> x = "a"
>>> "aa" is x * 2
False
>>> "aa" is intern(x*2)
True

Please see this question as well.