Why does assigning with [:] versus iloc[:] yield different results in pandas?

There is a very, very big difference between series.iloc[:] and series[:], when assigning back. (i)loc always checks to make sure whatever you're assigning from matches the index of the assignee. Meanwhile, the [:] syntax assigns to the underlying NumPy array, bypassing index alignment.

s = pd.Series(index=[0, 1, 2, 3], dtype='float')  
s                                                                          

0   NaN
1   NaN
2   NaN
3   NaN
dtype: float64

# Let's get a reference to the underlying array with `copy=False`
arr = s.to_numpy(copy=False) 
arr 
# array([nan, nan, nan, nan])

# Reassign using slicing syntax
s[:] = pd.Series([1, 2, 3, 4], index=['a', 'b', 'c', 'd'])                 
s                                                                          

0    1
1    2
2    3
3    4
dtype: int64

arr 
# array([1., 2., 3., 4.]) # underlying array has changed

# Now, reassign again with `iloc`
s.iloc[:] = pd.Series([5, 6, 7, 8], index=[3, 4, 5, 6]) 
s                                                                          

0    NaN
1    NaN
2    NaN
3    5.0
dtype: float64

arr 
# array([1., 2., 3., 4.])  # `iloc` created a new array for the series
                           # during reassignment leaving this unchanged

s.to_numpy(copy=False)     # the new underlying array, for reference                                                   
# array([nan, nan, nan,  5.]) 

Now that you understand the difference, let's look at what happens in your code. Just print out the RHS of your loops to see what you are assigning:

for i in range(2): 
    print(a_df.iloc[0, i*4:(i+1)*4]) 

# output - first row                                                                   
0    1
1    2
2    3
3    4
Name: 0, dtype: int64
# second row. Notice the index is different
4    5
5    6
6    7
7    8
Name: 0, dtype: int64   

When assigning to b_df.iloc[i, :] in the second iteration, the indexes are different so nothing is assigned and you only see NaNs. However, changing b_df.iloc[i, :] to b_df.iloc[i][:] will mean you assign to the underlying NumPy array, so indexing alignment is bypassed. This operation is better expressed as

for i in range(2):
    b_df.iloc[i, :] = a_df.iloc[0, i*4:(i+1)*4].to_numpy()

b_df                                                                       

   0  1  2  3
0  1  2  3  4
1  5  6  7  8

It's also worth mentioning this is a form of chained assignment, which is not a good thing, and also makes your code harder to read and understand.

The difference is that in the first case the Python interpreter executed the code as:

b_df.iloc[i,:] = a_df.iloc[0,i*4:(i+1)*4]
#as
b_df.iloc.__setitem__((i, slice(None)), value)

where the value would be the right hand side of the equation. Whereas in the second case the Python interpreter executed the code as:

b_df.iloc[i][:] = a_df.iloc[0,i*4:(i+1)*4]
#as
b_df.iloc.__getitem__(i).__setitem__(slice(None), value)

where again the value would be the right hand side of the equation.

In each of those two cases a different method would be called inside setitem due to the difference in the keys (i, slice(None)) and slice(None) Therefore we have different behavior.

Could anyone explain to me what the difference between .iloc[i,:] and .iloc[i][:] is

The difference between .iloc[i,:] and .iloc[i][:]

In the case of .iloc[i,:] you are accessing directly to a specific possition of the DataFrame, by selecting all (:) columns of the ith row. As far as I know, it is equivalent to leave the 2nd dimension unspecified (.iloc[i]).

In the case of .iloc[i][:] you are performing a 2 chained operations. So, the result of .iloc[i] will then be affected by [:]. Using this to set values is discouraged by Pandas itself here with a warning, so you shouldn't use it:

Whether a copy or a reference is returned for a setting operation, may depend on the context. This is sometimes called chained assignment and should be avoided

... and why .iloc[i][:] worked in my example above but not .iloc[i,:]

As @Scott mentioned on the OP comments, data alignment is intrinsic, so the indexes in the right side of the = won't be included if they are not present in the left side. This is why there are NaN values on the 2nd row.

So, to leave things clear, you could do as follows:

for i in range(2):
    # Get the slice
    a_slice = a_df.iloc[0, i*4:(i+1)*4]
    # Reset the indices
    a_slice.reset_index(drop=True, inplace=True)
    # Set the slice into b_df
    b_df.iloc[i,:] = a_slice

Or you can convert to list instead of using reset_index:

for i in range(2):
    # Get the slice
    a_slice = a_df.iloc[0, i*4:(i+1)*4]
    # Convert the slice into a list and set it into b_df
    b_df.iloc[i,:] = list(a_slice)