Tablets have moved fully from novelties to productive devices, and most everyone who doesn't have a tablet website (or, as applicable, app) wants one.
A trend, at least in clients I see and hear about, is to consider the tablet as just a Desktop With Touch.
It's certainly good in that tablets aren't being forgotten, but they aren't really being considered as separate devices either. Very often, the touch-friendly interface is not unique to the tablet, but just part of the desktop website version.
But mobile is different. Okay, yes, there are totally people who are saying "mobile" means a handset. There are a few who say MIDs (e.g. iPod Touch) don't count, because they have no voice connectivity. There are interesting behavioral differences in the way a 10" tablet is used, vs. a 7" tablets, vs. a 4-5" handset/MID.
But I still think this is totally looking at it the wrong way. Because the gap between any one of these is nothing compared to the gulf between any of them and any desktop. Desktops, and laptops, and even the portable, touchscreen Tablet PC, is a basically stupid device that does pretty much nothing unless you ask it, and still is more involved in it's own inner workings and processes than in helping you. A desktop is a benevolent bureaucracy.
The mobile, whatever it's size or guise, is a family member. It loves and cares for you. It knows who you are, and can tell where you are and what you are doing. Whether with you all the time, your companion on the train, or sitting patiently on the coffee table at home, it is on and connected and waiting to talk to you about the latest happenings with your friends, and remind you it's time to schedule a dentist appointment.
Okay, even if you agree, you might say "how can I use this?"
Well, use your device capabilities, and tie them to your needs. A good opportunity to me is the relentless use of username/password to authenticate on mobile. We don't use that on ATMs, or when we call customer care, or talk to someone face to face. It's a desktop-web solution lazily applied to a totally new interface. What's the mobile answer? Well, no one's looked into it enough, but certainly something else. No one has really done it. Voice? Gesture? How about adding security by using photo and location sensors to add an audit trail unlike anything we've had in desktop computing.
Or, a lot of folks I work with get lost when trying to figure out how a 7" tablet will fit in their strategy. I don't get the problem. For one good starting point, lay them on top of each other; a 7" tablet is broadly the same width in landscape as a 10" tablet in portrait. Your app or site works in portrait on iPad, right? So, how hard can it be to just stick that on the 7" and let the user scroll a bit more. The best part: you can probably do this sort of design with responsive principles and just set rules for flow and scale, instead of designing for 7" tablets, or 5.3" handsets.
Sure, specialized tools (drawing, games) may need special interfaces, but they also didn't generally have 10" tablet interfaces a couple years ago. We have to be adaptable, and not try to shove everything new into an existing cubbyhole.
For any device, consider the capabilities, the way users employ them differently, and design your interface by classes to react to all of these, for the best experience with the least one-off design.