Similar to @locojay suggestion, you can apply difflib‘s get_close_matches to df2‘s index and then apply a join:
In [23]: import difflib
In [24]: difflib.get_close_matches
Out[24]: <function difflib.get_close_matches>
In [25]: df2.index = df2.index.map(lambda x: difflib.get_close_matches(x, df1.index)[0])
In [26]: df2
Out[26]:
letter
one a
two b
three c
four d
five e
In [31]: df1.join(df2)
Out[31]:
number letter
one 1 a
two 2 b
three 3 c
four 4 d
five 5 e
.
If these were columns, in the same vein you could apply to the column then merge:
df1 = DataFrame([[1,'one'],[2,'two'],[3,'three'],[4,'four'],[5,'five']], columns=['number', 'name'])
df2 = DataFrame([['a','one'],['b','too'],['c','three'],['d','fours'],['e','five']], columns=['letter', 'name'])
df2['name'] = df2['name'].apply(lambda x: difflib.get_close_matches(x, df1['name'])[0])
df1.merge(df2)