BUG: "unique" and pd.Series.unique produce different results with aggregation
- [x] I have checked that this issue has not already been reported.

- [x] I have confirmed this bug exists on the latest version of pandas.

- [x] (optional) I have confirmed this bug exists on the master branch of pandas.

---

#### Code Sample, a copy-pastable example

```python
import pandas as pd

df = pd.DataFrame({"a": [1, 2, 1, 2], "b": [2, 1, 1, 2]})
g = df.groupby("a")

for aggfunc in ["unique", pd.unique, pd.Series.unique]:
    try:
        print(g.agg({"b": aggfunc}))
    except ValueError as e:
        print(f"{aggfunc!r} failed with {e!r}")
```

Running this script produces

```
        b
a        
1  [2, 1]
2  [1, 2]
<function unique at 0x7f6885cc7310> failed with ValueError('Must produce aggregated value')
<function Series.unique at 0x7f688369f8b0> failed with ValueError('Must produce aggregated value')
```

#### Problem description

When using "unique" str as the `aggfunc` parameter, internally it is [interpreted](https://github.com/pandas-dev/pandas/blob/v1.2.2/pandas/core/groupby/generic.py#L241) as `pd.Series.unique`. I expect identical results when passing "unique" and `pd.Series.unique`, or `pd.unique` but they are not.

#### Output of ``pd.show_versions()``

<details>

INSTALLED VERSIONS
------------------
commit           : f904213ffcc36d3ae29c37ae28fbb1844a0769ab
python           : 3.9.1.final.0
python-bits      : 64
OS               : Linux
OS-release       : 5.10.11-arch1-1
Version          : #1 SMP PREEMPT Wed, 27 Jan 2021 13:53:16 +0000
machine          : x86_64
processor        :
byteorder        : little
LC_ALL           : None
LANG             : en_US.UTF-8
LOCALE           : en_US.UTF-8

pandas           : 1.3.0.dev0+772.gf904213ffc
numpy            : 1.20.1
pytz             : 2021.1
dateutil         : 2.8.1
pip              : 20.2.3
setuptools       : 49.2.1
Cython           : None
pytest           : None
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
fsspec           : None
fastparquet      : None
gcsfs            : None
matplotlib       : None
numexpr          : None
odfpy            : None
openpyxl         : None
pandas_gbq       : None
pyarrow          : None
pyxlsb           : None
s3fs             : None
scipy            : None
sqlalchemy       : None
tables           : None
tabulate         : None
xarray           : None
xlrd             : None
xlwt             : None
numba            : None

</details>
