defining/non defining relative clause

In these 2 sentence:

  1. The man gave his money to the charity, which he preferred.
  2. The man gave his money to the charity which he preferred.
    Is there a difference between these 2 sentences apart from the commas, of course?
    Thank you for your time!

#1 seems like an imperfect way of saying that he preferred to give his money to charity rather than doing something else with it.

#2 means that he gave the money to his preferred charity. I prefer to use “that” for defining clauses like this one, but some people do not care about this distinction.