Originally Posted by Sid70

firm2    
[furm] Show IPA
?noun
1.
a partnership or association for carrying on a business.
2.
the name or title under which associated parties transact business: the firm of Smith & Jones.


................



com·pa·ny   
[kuhm-puh-nee] Show IPA
noun, plural -nies, verb, -nied, -ny·ing.
?noun
1.
a number of individuals assembled or associated together; group of people.
2.
a guest or guests: We're having company for dinner.
3.
an assemblage of persons for social purposes.



So a firm certainly means bbusiness while compnay can be just a group of people.
But I think it doesnt matter much in context where buisnes services involved.