I'm a social media/digital marketing consultant so can maybe shed some light!
The best analogy I've heard for the three big platforms (FB, Twitter, Linkedin) is:
Facebook is like a dinner party
Twitter is like a cocktail party
Linkedin is like a networking party
Mostly because LI is set up for professional networking/ thought leadership etc. Facebook is private behind a login and the set up allows for longer posting, linked conversation threads etc. Twitter is completely public - you can talk to anyone, anyone can talk to you. (Though now I think you can make your profile private to stop people following you.)
Even me, the so-called professional, struggled to get to grips with Twitter. But then the riots in Egypt happened a few years back, and saw how amazing it was a tool to get information out of a country where information and communication was locked down. I ended up Tweeting myself well into the early hours on behalf of my company during the London riots. My local Twitter person - someone in my area set up a XXX-location account to tweet stuff about our area - also provided valuable information on what was happening, how close trouble was etc. It's also awesome for other, less threatening real-time information - like train line feeds.
I reckon Twitter is set up better for businesses - BTB, commercial, small business, consultancy and self-employed people do very well to use it as a brand awareness tool. But I have a lot of friends who simply just delight in "talking" to celebrities - like, never before have us - lowly civilians - been able to actually talk to people in the public eye. I have other friends who use it like FB - except their conversations are ultra public, and I don't really get why they use it like that.
I've also had some great success publicly scolding companies who have had shocking customer services, and the results have always been good because companies simply can't afford to let stuff like that go unaddressed. Basically - the consumer has found its voice and its not afraid to use it! Even Fitness First crumbled and I've always had such problems with them.
Except - you're free to use it however the heck you like! That's kind of the beauty of it. It's not restrictive like FB. There's a gazillion add on tools like tweet extensions, image posting, etc. Mooch around, find your friends, or people you like in the public eye, or companies you like, see what everyone else does and find your way :)