Hi, this depends on the jurisdiction you are using this word. One of the main differences is a company is a legal entity (e.g. has limited liability) but a firm can be a description for a different number of legal entities. For example, a partnership can be a firm, but it cannot be a company.

In everyday situations, firm usually is used to describe businesses that offer services in accounting, law, or some other professional consulting work. I see now after Googling, that there are some specific differences between them relating to tax law that I don't fully understand. https://smallbusiness.chron.com/differences-between-firm-company-establishment-33208.html