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

is will return True if two variables point to the same object, == 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.

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 there a difference between == and is in Python?

Yes, they have a very important difference.

==: check for equality - the semantics are that equivalent objects (that aren't necessarily the same object) will test as equal. As the documentation says:

The operators <, >, ==, >=, <=, and != compare the values of two objects.

is: check for identity - the semantics are that the object (as held in memory) is the object. Again, the documentation says:

The operators is and is not test for object identity: x is y is true if and only if x and y are the same object. Object identity is determined using the id() function. x is not y yields the inverse truth value.

Thus, the check for identity is the same as checking for the equality of the IDs of the objects. That is,

a is b

is the same as:

id(a) == id(b)

where id is the builtin function that returns an integer that "is guaranteed to be unique among simultaneously existing objects" (see help(id)) and where a and b are any arbitrary objects.

Other Usage Directions

You should use these comparisons for their semantics. Use is to check identity and == to check equality.

So in general, we use is to check for identity. This is usually useful when we are checking for an object that should only exist once in memory, referred to as a "singleton" in the documentation.

Use cases for is include:

None
enum values (when using Enums from the enum module)
usually modules
usually class objects resulting from class definitions
usually function objects resulting from function definitions
anything else that should only exist once in memory (all singletons, generally)
a specific object that you want by identity

Usual use cases for == include:

numbers, including integers
strings
lists
sets
dictionaries
custom mutable objects
other builtin immutable objects, in most cases

The general use case, again, for ==, is the object you want may not be the same object, instead it may be an equivalent one

PEP 8 directions

PEP 8, the official Python style guide for the standard library also mentions two use-cases for is:

Comparisons to singletons like None should always be done with is or is not, never the equality operators.

Also, beware of writing if x when you really mean if x is not None -- e.g. when testing whether a variable or argument that defaults to None was set to some other value. The other value might have a type (such as a container) that could be false in a boolean context!

Inferring equality from identity

If is is true, equality can usually be inferred - logically, if an object is itself, then it should test as equivalent to itself.

In most cases this logic is true, but it relies on the implementation of the __eq__ special method. As the docs say,

The default behavior for equality comparison (== and !=) is based on the identity of the objects. Hence, equality comparison of instances with the same identity results in equality, and equality comparison of instances with different identities results in inequality. A motivation for this default behavior is the desire that all objects should be reflexive (i.e. x is y implies x == y).

and in the interests of consistency, recommends:

Equality comparison should be reflexive. In other words, identical objects should compare equal:

x is y implies x == y

We can see that this is the default behavior for custom objects:

>>> class Object(object): pass
>>> obj = Object()
>>> obj2 = Object()
>>> obj == obj, obj is obj
(True, True)
>>> obj == obj2, obj is obj2
(False, False)

The contrapositive is also usually true - if somethings test as not equal, you can usually infer that they are not the same object.

Since tests for equality can be customized, this inference does not always hold true for all types.

An exception

A notable exception is nan - it always tests as not equal to itself:

>>> nan = float('nan')
>>> nan
nan
>>> nan is nan
True
>>> nan == nan           # !!!!!
False

Checking for identity can be much a much quicker check than checking for equality (which might require recursively checking members).

But it cannot be substituted for equality where you may find more than one object as equivalent.

Note that comparing equality of lists and tuples will assume that identity of objects are equal (because this is a fast check). This can create contradictions if the logic is inconsistent - as it is for nan:

>>> [nan] == [nan]
True
>>> (nan,) == (nan,)
True

A Cautionary Tale:

The question is attempting to use is to compare integers. You shouldn't assume that an instance of an integer is the same instance as one obtained by another reference. This story explains why.

A commenter had code that relied on the fact that small integers (-5 to 256 inclusive) are singletons in Python, instead of checking for equality.

Wow, this can lead to some insidious bugs. I had some code that checked if a is b, which worked as I wanted because a and b are typically small numbers. The bug only happened today, after six months in production, because a and b were finally large enough to not be cached. – gwg

It worked in development. It may have passed some unittests.

And it worked in production - until the code checked for an integer larger than 256, at which point it failed in production.

This is a production failure that could have been caught in code review or possibly with a style-checker.

Let me emphasize: do not use is to compare integers.

== determines if the values are equal, while is determines if they are the exact same object.

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