A Facebook profile is for individuals, not companies. The profile is under your personal name, and it's against Facebook's terms of service to use a company name for your Facebook profile. Although you can post content about your company on your profile, this is not a good way to market your company on Facebook. Why is this?
A Facebook page is a page you create in Facebook for your company or an interest (such as a brand of merchandise you like, an artist or band of which you're a fan, etc.) A Facebook page is publicly viewable from not only other Facebook members, but non-members as well. Content that you post on the page can also get indexed by search engines, which makes it great for marketing your company. The page is separate from your personal profile (although you manage your page by logging in from your personal profile), so people who view and "like" your page can only see the page content (posts, photos, etc.); it has no effect on your personal profile, and people can't even see that it's associated with your personal profile.
With a Facebook page you can assign other people to manage or create content for the page, which you cannot (and should not) do with a profile (as you would have to give them your Facebook username and password). This makes a Facebook page the obvious choice for companies with more than one employee who will be making changes to the page.
Facebook pages do not have "friends" the way your profile does. Instead, Facebook pages get "likes". Although anyone can view the page whether they've liked it or not, if they "like" the page, then any content you post on the page automatically appears in their news feed. Depending on how they have their privacy settings set up, the post may also appear on their friends' news feeds, or friends of friends. So one post on your page could reach hundreds or thousands of Facebook users. But how do you get likes from people other than friends and family? You utilize Facebook ads to reach people in your target demographic!
A Facebook Group is ideal for communication within a group or community, for instance your local book club or townhouse community. In order for someone to join a Facebook group, someone in the group (usually the group administrator) must approve the request. Group content does not show up in search engines, whereas pages do. And posts made within a group do not show on the member's news feed like page posts do. For these reasons, a Facebook Group is not the ideal way to market your business unless you're making lots of posts to communicate specifically with the people in the group.