There are so many different types of law firms; I don't think I could identify all of them. There are general firms that offer many different types of legal services and boutique firms that specialize in a specific area. There are also people who hang their own "shingle" and offer their services as an individual attorney.
There are firms for companies and firms for individuals. For example, firms for companies help the companies with forming a corporation, getting loans/financing, filing reports required by the government, drafting and negotiating contracts, give employment or tax advice, and managing law suits.
Firms that work with individuals can work on a range of issues: family issues (divorce, custody, etc.), wills, immigration, personal injuries (like car accidents), tax advice, discrimination, criminal investigations, etc.
Take some time to explore what interests you and to figure out what you're good at. I negotiate contracts for technology companies. I've never stepped foot in a court room and my mom says I'm not useful to her. But I love what I do and think I'm pretty good at it.