I think the "How do I become a consultant/start a consulting business" comes up every few months. Here is what I've taken from those posts. There is a difference between consulting and freelancing. Consultants are people who come in and help make decision and Freelancers are people who make those decisions happen (aka contractors).
(I personally do both, and honestly have more fun 'freelancing' than 'consulting').
The connotation that "freelancer" carries is that you are in general someone who can be plugged into an arbitrary dev project instead of an FTE. When you hear "freelancer", think instead "temp". Highly-paid temp! But: temp. Also: a freelancer is usually a sole proprietor; when you get 3 freelancers into a room, they become "contractors". Same connotation.
A consultant is someone whose practice is so expensive that for most companies it would make zero sense to keep them on staff. Think about graphic designers. I love graphic design and I love paying for graphic design, but I will never be able to convince Dave & Jeremy that we should hire a full time graphic designer. (And here you get a small taste of the complexity of the word "expensive", since graphic design is in reality very cheap).
There is a blurry line between consultants and freelancers/contractors. Sometimes, consultants get sucked into contractor projects; these are commonly called "staff augmentation" projects. You do them because you like the client and because the money is usually good; also, sometimes the market for whatever you do heats up, and suddenly it starts to make fiscal sense for lots of different companies to effectively get a full-time body to do what you do.
(I personally do both, and honestly have more fun 'freelancing' than 'consulting').