> So essentially it's a sales technique.
I've worked as a freelancer and with consultants and I think your problem is that you're focusing on the website. These businesses receive Zero (0) inbounds from their websites. The reason why they even have a website is because, well, it's 2015. It might be a window into how the business works but changing your freelance website to look like a consultancy would make no difference whatsoever.
What divides the two is their professional networks: where they find business, who they're working for, and why. Freelancers try to drum up business by going to meetups, following up on weak leads ("I hear Jim needs a new website") subcontracting through agencies. Their value proposition is that they do an hour's work for an hours pay and they're in business for themselves most likely cause they're just trying to escape the cube farm.
A consultant got into her business because she's realized that she's reached the peak of what she can make as an "individual contributor". She has a big book of business before she even hangs out her shingle and perhaps decided to start consulting because she had too many people wanting to give her money and didn't want to commit to one. Her client list grows organically through referrals being made through her huge professional network. When she enters into sales negotiations the impetus is on the client to sale the gig to her rather than the other way around.
I would like to work for myself again but not as a freelancer. That's a dead-end world. My goal now is to either develop my career to the point where I can be a proper consultant or (even better) develop a SaaS product.