Pandas BUG: describe does not distinguish between Int64 and int64

Pandas version checks

• [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] I have confirmed this bug exists on the main branch of pandas.

Reproducible Example

df = pd.DataFrame({"A": pd.Series([1,2,3], dtype="Int64"), "B": pd.Series([1,2,3], dtype="int64")})
df.describe(include="int64")

         A    B
count  3.0  3.0
mean   2.0  2.0
std    1.0  1.0
min    1.0  1.0
25%    1.5  1.5
50%    2.0  2.0
75%    2.5  2.5
max    3.0  3.0

```

Issue Description

Should only include B, not both

Expected Behavior

remove A from result

Installed Versions

main

Comment From: jbrockmendel

Notes for whoever comes along to handle this:

1) In infer_dtype_from_object there is a kludge for BaseMaskedDtype if hasattr(dtype, "numpy_dtype"): 2) In select_dtypes there is a kludge for ArrowDtype

I expect resolving this issue will require a significant surgery on these two functions, so avoiding these kludges should be part of the goal.

Comment From: phofl

Yes, the kludge was a necessary fix for 2.0.1