In Python, what is the difference between ".append()" and "+= []"?

>>> a=[]
>>> a.append([1,2])
>>> a
[[1, 2]]
>>> a=[]
>>> a+=[1,2]
>>> a
[1, 2]

See that append adds a single element to the list, which may be anything. +=[] joins the lists.

For your case the only difference is performance: append is twice as fast.

Python 3.0 (r30:67507, Dec  3 2008, 20:14:27) [MSC v.1500 32 bit (Intel)] on win32
Type "help", "copyright", "credits" or "license" for more information.
>>> import timeit
>>> timeit.Timer('s.append("something")', 's = []').timeit()
0.20177424499999999
>>> timeit.Timer('s += ["something"]', 's = []').timeit()
0.41192320500000079

Python 2.5.1 (r251:54863, Apr 18 2007, 08:51:08) [MSC v.1310 32 bit (Intel)] on win32
Type "help", "copyright", "credits" or "license" for more information.
>>> import timeit
>>> timeit.Timer('s.append("something")', 's = []').timeit()
0.23079359499999999
>>> timeit.Timer('s += ["something"]', 's = []').timeit()
0.44208112500000141

In general case append will add one item to the list, while += will copy all elements of right-hand-side list into the left-hand-side list.

Update: perf analysis

Comparing bytecodes we can assume that append version wastes cycles in LOAD_ATTR + CALL_FUNCTION, and += version -- in BUILD_LIST. Apparently BUILD_LIST outweighs LOAD_ATTR + CALL_FUNCTION.

>>> import dis
>>> dis.dis(compile("s = []; s.append('spam')", '', 'exec'))
  1           0 BUILD_LIST               0
              3 STORE_NAME               0 (s)
              6 LOAD_NAME                0 (s)
              9 LOAD_ATTR                1 (append)
             12 LOAD_CONST               0 ('spam')
             15 CALL_FUNCTION            1
             18 POP_TOP
             19 LOAD_CONST               1 (None)
             22 RETURN_VALUE
>>> dis.dis(compile("s = []; s += ['spam']", '', 'exec'))
  1           0 BUILD_LIST               0
              3 STORE_NAME               0 (s)
              6 LOAD_NAME                0 (s)
              9 LOAD_CONST               0 ('spam')
             12 BUILD_LIST               1
             15 INPLACE_ADD
             16 STORE_NAME               0 (s)
             19 LOAD_CONST               1 (None)
             22 RETURN_VALUE

We can improve performance even more by removing LOAD_ATTR overhead:

>>> timeit.Timer('a("something")', 's = []; a = s.append').timeit()
0.15924410999923566

In the example you gave, there is no difference, in terms of output, between append and +=. But there is a difference between append and + (which the question originally asked about).

>>> a = []
>>> id(a)
11814312
>>> a.append("hello")
>>> id(a)
11814312

>>> b = []
>>> id(b)
11828720
>>> c = b + ["hello"]
>>> id(c)
11833752
>>> b += ["hello"]
>>> id(b)
11828720

As you can see, append and += have the same result; they add the item to the list, without producing a new list. Using + adds the two lists and produces a new list.