BUG: Incorrect factorization for ordinal vs nominal variable
### 

- [X] I have checked that this issue has not already been reported.

- [X] I have confirmed this bug exists on the [latest version](https://pandas.pydata.org/docs/whatsnew/index.html) of pandas.

- [X] I have confirmed this bug exists on the master branch of pandas.


### Reproducible Example

```python
<CASE 1>
import pandas as pd
cat = pd.Categorical(['a', 'a', 'c'], categories=['a', 'b', 'c'])
codes, uniques = pd.factorize(cat)
codes
>>> Output-: array([0, 0, 1], dtype=int64)
<CASE 2>
import pandas as pd
cat = pd.Categorical(['a', 'a', 'c'], categories=['a', 'b', 'c'], ordered=True)
codes, uniques = pd.factorize(cat)
codes
>>> Output-: array([0, 0, 1], dtype=int64)
```


### Issue Description

In case 1 when we define a nominal variable we get the factorized values as [0,0,1] which seems fine but in case 2 when the variable is ordinal we get the same output i.e. [0,0,1]

### Expected Behavior

But instead, we should have got the output as [0,0,2]

### Installed Versions

<details>

INSTALLED VERSIONS
------------------
commit           : 5f648bf1706dd75a9ca0d29f26eadfbb595fe52b
python           : 3.8.11.final.0
python-bits      : 64
OS               : Windows
OS-release       : 10
Version          : 10.0.19042
machine          : AMD64
processor        : Intel64 Family 6 Model 165 Stepping 2, GenuineIntel
byteorder        : little
LC_ALL           : None
LANG             : None
LOCALE           : English_India.1252

pandas           : 1.3.2
numpy            : 1.20.3
pytz             : 2021.1
dateutil         : 2.8.2
pip              : 21.2.4
setuptools       : 52.0.0.post20210125
Cython           : None
pytest           : 6.2.4
hypothesis       : None
sphinx           : None
blosc            : None
feather          : None
xlsxwriter       : None
lxml.etree       : 4.6.3
html5lib         : None
pymysql          : None
psycopg2         : None
jinja2           : 3.0.1
IPython          : 7.26.0
pandas_datareader: None
bs4              : 4.9.3
bottleneck       : 1.3.2
fsspec           : 2021.07.0
fastparquet      : None
gcsfs            : None
matplotlib       : 3.4.2
numexpr          : 2.7.3
odfpy            : None
openpyxl         : None
pandas_gbq       : None
pyarrow          : None
pyxlsb           : None
s3fs             : None
scipy            : 1.7.1
sqlalchemy       : None
tables           : None
tabulate         : None
xarray           : None
xlrd             : None
xlwt             : None
numba            : 0.54.0

</details>
