Why does pandas.DataFrame.groupby(function) work when the function returns the Timestamp.date method itself instead of calling it?

In the following example, pandas.Dataframe.groupby() works the same whether or not the date() method of the timestamp is explicitly called. Why? I expected the explicit call to be required.

import pandas as pd

def return_date_method(timestamp):
    return timestamp.date

def call_date_method(timestamp):
    return timestamp.date()

df = pd.DataFrame(range(4),
                  index=pd.date_range('2022', freq='12h', periods=4))

print(f'Using Pandas version {pd.__version__}')
print(df)
print()
print('return_date_method(df.index[0]) returns', return_date_method(df.index[0]))
print('call_date_method(df.index[0]) returns', call_date_method(df.index[0]))
print()
print(df.groupby(return_date_method).groups)
print()
print(df.groupby(call_date_method).groups)

Output:

Using Pandas version 0.25.3
                     0
2022-01-01 00:00:00  0
2022-01-01 12:00:00  1
2022-01-02 00:00:00  2
2022-01-02 12:00:00  3

return_date_method(df.index[0]) returns <built-in method date of Timestamp object at 0x00000233478574C8>
call_date_method(df.index[0]) returns 2022-01-01

{datetime.date(2022, 1, 1): DatetimeIndex(['2022-01-01 00:00:00', '2022-01-01 12:00:00'], dtype='datetime64[ns]', freq='12H'), datetime.date(2022, 1, 2): DatetimeIndex(['2022-01-02 00:00:00', '2022-01-02 12:00:00'], dtype='datetime64[ns]', freq='12H')}

{datetime.date(2022, 1, 1): DatetimeIndex(['2022-01-01 00:00:00', '2022-01-01 12:00:00'], dtype='datetime64[ns]', freq='12H'), datetime.date(2022, 1, 2): DatetimeIndex(['2022-01-02 00:00:00', '2022-01-02 12:00:00'], dtype='datetime64[ns]', freq='12H')}

This example shows that the behavior is different when using str.isalpha().

def return_isalpha_method(string):
    return string.isalpha

def call_isalpha_method(string):
    return string.isalpha()

df2 = pd.DataFrame(range(4), index=list('1a2b'))
print(df2)
print()
print(df2.groupby(call_isalpha_method).groups)
print()
try:
    print(df2.groupby(return_isalpha_method).groups)
except TypeError as exception:
    print('TypeError:', exception)

Output:

   0
1  0
a  1
2  2
b  3

{False: Index(['1', '2'], dtype='object'), True: Index(['a', 'b'], dtype='object')}

TypeError: '<' not supported between instances of 'builtin_function_or_method' and 'builtin_function_or_method'