reindex_like(s, method='ffill') is different than reindex_like(s).fillna(method='ffill')

[actual-panda]

I don't know whether this a bug or a feature, but the behavior is not clear to me after reading the reindex_like docs.

There is a note "Please note: this is only applicable to DataFrames/Series with a monotonically increasing/decreasing index." - but what it actually does is to fill "as if" the index after reindexing was sorted.

Sample code

>>> import pandas as pd
>>> s1 = pd.Series(['[0, 1)', '[1, 3)', '[3, 4)', '[4, 6)', '[6, inf)'], index=[0, 1, 3, 4, 6], dtype='string')
>>> s2 = pd.Series(['']*8, index=[6, 2, 5, 0, 4, 7, 1, 3], dtype='string')
>>>
>>> s1
0      [0, 1)
1      [1, 3)
3      [3, 4)
4      [4, 6)
6    [6, inf)
dtype: string
>>> s2
6    
2    
5    
0    
4    
7    
1    
3    
dtype: string
>>> s1.reindex_like(s2).fillna(method='ffill')
6    [6, inf)
2    [6, inf)
5    [6, inf)
0      [0, 1)
4      [4, 6)
7      [4, 6)
1      [1, 3)
3      [3, 4)
dtype: string
>>> s1.reindex_like(s2, method='ffill')
6    [6, inf)
2      [1, 3)
5      [4, 6)
0      [0, 1)
4      [4, 6)
7    [6, inf)
1      [1, 3)
3      [3, 4)
dtype: string

I expected the same result with both methods. Should they behave differently?

Output of pd.show_versions()

INSTALLED VERSIONS

commit : None
python : 3.8.1.final.0
python-bits : 64
OS : Windows
OS-release : 10
machine : AMD64
processor : Intel64 Family 6 Model 142 Stepping 10, GenuineIntel
byteorder : little
LC_ALL : None
LANG : None
LOCALE : de_DE.cp1252
pandas : 1.0.3
numpy : 1.18.4
pytz : 2020.1
dateutil : 2.8.1
pip : 20.0.2
setuptools : 45.2.0
Cython : None
pytest : 5.4.2
hypothesis : None
sphinx : None
blosc : None
feather : None
xlsxwriter : None
lxml.etree : None
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : None
IPython : None
pandas_datareader: None
bs4 : None
bottleneck : None
fastparquet : None
gcsfs : None
lxml.etree : None
matplotlib : None
numexpr : None
odfpy : None
openpyxl : None
pandas_gbq : None
pyarrow : None
pytables : None
pytest : 5.4.2
pyxlsb : None
s3fs : None
scipy : None
sqlalchemy : None
tables : None
tabulate : None
xarray : None
xlrd : None
xlwt : None
xlsxwriter : None
numba : None

[tomytp]

I believe this can be closed following the merge of pull request:
#58724