The expressions mean something different:
感冒
To catch a cold is to catch the disease.
着凉
To catch cold, or to take cold is to stay out too long in cold weather and
spend a long time shivering afterwards. The experience may cause you to catch
a cold, but not necessarily.
https://forum.wordreference.com/threads/catch-a-cold-or-catch-cold.724722/
catch cold
in American English
take cold
to get or suffer from a cold
We all caught cold during that dreadful winter
https://www.collinsdictionary.com/dictionary/english/catch-cold
catch cold/catch a cold
If you catch cold, or catch a cold, you become ill with a cold.
Let's dry our hair so we don't catch cold.
https://www.collinsdictionary.com/dictionary/english/catch-cold-catch-a-cold