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Reproducible Example

import pandas as pd

series = pd.Categorical(['A', 'B', 'C'])
print(f"is_string_dtype(series): {pd.api.types.is_string_dtype(series)}") # True  
print(f"is_string_dtype(series.dtype): {pd.api.types.is_string_dtype(series.dtype)}") # False

Issue Description

pd.api.types.is_string_dtype() returns inconsistent results when passed a Categorical series directly versus the dtype of that series.

Expected Behavior

IMO, both calls should return False since a Categorical is not a string dtype.

Installed Versions

INSTALLED VERSIONS ------------------ commit : c888af6d0bb674932007623c0867e1fbd4bdc2c6 python : 3.11.0 python-bits : 64 OS : Darwin OS-release : 24.3.0 Version : Darwin Kernel Version 24.3.0: Thu Jan 2 20:24:23 PST 2025; root:xnu-11215.81.4~3/RELEASE_ARM64_T8122 machine : arm64 processor : arm byteorder : little LC_ALL : None LANG : None LOCALE : None.UTF-8 pandas : 2.3.1 numpy : 2.3.1 pytz : 2025.2 dateutil : 2.9.0.post0 pip : 25.0.1 Cython : None sphinx : None IPython : 9.4.0 adbc-driver-postgresql: None adbc-driver-sqlite : None bs4 : 4.13.4 blosc : None bottleneck : None dataframe-api-compat : None fastparquet : None fsspec : 2025.3.0 html5lib : None hypothesis : 6.138.0 gcsfs : 2025.3.0 jinja2 : 3.1.6 lxml.etree : None matplotlib : 3.10.1 numba : None numexpr : None odfpy : None openpyxl : None pandas_gbq : None psycopg2 : None pymysql : None pyarrow : 19.0.1 pyreadstat : None pytest : 8.3.5 python-calamine : None pyxlsb : None s3fs : 2025.3.0 scipy : 1.15.2 sqlalchemy : 2.0.39 tables : None tabulate : 0.9.0 xarray : 2025.6.1 xlrd : None xlsxwriter : None zstandard : None tzdata : 2025.2 qtpy : None pyqt5 : None