How to substract two dataframe when index does not exactly match the index of the other data frame

Given:

DF1 = pd.DataFrame({'Val':[5, 5, 5, 5, 5, 5, 5]}, index=[0, 1, 2, 3, 4, 5, 6])

DF2 = pd.DataFrame({'Val':[2, 2, 2, 2]}, index=[0, 1, 2, 3])

DF3 = pd.DataFrame({'Val':[5, 5, 5, 5, 5, 5, 5, 5]}, index=[0, 1, 2, 3, 4, 5, 6, 7])

You can do:

DF1['Val'].subtract(DF2['Val'].reindex(DF1.index, fill_value=0))

0    3
1    3
2    3
3    3
4    5
5    5
6    5
Name: Val, dtype: int64

For your second question, it's the opposite:

DF1['Val'].reindex(DF2.index, fill_value=0).subtract(DF2['Val'])

0    0
1    0
2    0
3    0
4    0
5    0
6    0
7   -5
Name: Val, dtype: int64

EDIT: For the more complex case (where there is an index overlap but one is not a subset of the other):

DF4 = pd.DataFrame({'Val':[5, 5]}, index=[4, 5])

DF5 = pd.DataFrame({'Val':[5, 5, 5]}, index=[5, 6, 7])

common_index = DF4.index.union(DF5.index)
DF4['Val'].reindex(common_index, fill_value=0).subtract(DF5['Val'].reindex(common_index, fill_value=0))

4    5
5    0
6   -5
7   -5
Name: Val, dtype: int64