Yes, I agree. No real difference, especially in contexts other than contracts, or other corporate papers. Law firm sounds slightly more prestigious (on a resume).To me, "law office" and "law firm" mean the same thing. The definite article is optional before the name, because "the" refers to the noun, "firm."
"He worked for Jones and Smith."
"He worked for Jones and Smith law firm."
"He worked for the Jones and Smith law firm."
"He worked for the law firm of Jones and Smith."
In general, you would not use "the" before a name.
"He was an engineer for Chrysler Motors." Not, "He was an engineer for the Chrysler Motors." You could say, "He was an engineer for the Chrysler Motors Corporation."
I agree. In the US when you make a phone call to a lawyer's office/law firm, it is common for the person who answers the phone to say, "Law office(s)". He/she probably would not say, "Law firm". It is also common to say the full name of the firm, as in "Dewey, Jenkins, Fingerbutter, Cheatham, and Steel". The secretary has repeated the name hundreds of times and says it really fast. It is so fast that the person making the call doesn't understand a word.A law firm is a business.
A law office is a place.