"Take a hotel experience for example. You don't expect the hotel's ad, website and front desk clerk to all say the same thing. It matters much less if they are consistent with each other than it matters that they complement each other, reinforcing each others' messages to create an interesting story."
Now I'm not qualified to talk about brands, and having worked through the dot-com years I feel that I've developed a pavlovian aversion to the word, but this is freakishly close to an analogy that I've used in the past: banks. You deal with your bank in many different ways - on the phone, on the net (perhaps), using an ATM, or in person at your branch.
In each of these ways, you go through an entirely different set of actions, to, say, check your balance: on the phone I give my name, some other details, and 2 digits of a password. At an ATM I enter my card and type a PIN. In a branch I give my card (or account number) and sign a slip of paper.
And yet at the same time, your experience is consistent: you're identifying yourself, requesting an operation (using the banks language, no less: "deposit", "balance", "withdrawal") and getting it done.
And this is an analogy which I believe shows the way for mobile apps: they won't be the same as web or other channels, and you may ask people to do different (but complementary) tasks, in order to realise a set of goals which is consistent with their experience elsewhere. As well as consistency of goal, congruent use of tone and terminology can emphasise the "sameness" of what your customers are doing, whilst you have them actually do it in a way that's completely in context with how they're choosing to talk to you.