One of the fundamental assumptions of all training (except perhaps on-the-job training) is that people have the ability to port contexts. In other words, they can see and understand and get good at something in a training context, and can then apply that learning where it is supposed to be applied -- in the different context of their work. This ability to transfer is probably uniquely human -- you can show Fido videos of someone throwing a ball for a dog all day, but when you then throw the first real ball for him he'll look at you as if you are mad.
In an online mode, unless you are teaching computer-related skills, perhaps we call for a greater leap of the imagination than in a classroom mode. Everything we see and do is in two dimensions on a flat screen. Making the leap from the truly virtual online world to the totally real workplace world may be heroic for some. Or maybe not -- the past few years have seen such a surge in computer proficiency that maybe people feel more comfortable than they did before.
On a more practical note, there's a bunch of assumptions. Sometimes we make them, other times we are smart enough not to assume, others we design around.
We often assume that online learners have a lot more ability to concentrate than they do in reality. We assume a relatively quiet interruption-free learning environment. We assume that they have the will and the motivation to push through the work without a classroom pace-setter. We assume people want to work at their own pace in a time convenient to them, rather than being led by someone else's schedule. We assume that learners are comfortable with all of the alarming personal privacy issues that online learning potentially exposes them to. We tend to assume a particular technology platform for online learners (operating system, browser version, plug-ins, bandwidth, performance) that in my experience is often way off the mark. We assume people read e-mails. We assume people want to take the courses they are taking. We assume either that they need to be led down a predetermined path mapped out by an instructional designer, or that they want to be able to find their own way. We assume that they want to finish what they started. And we assume that all of the unscripted "fuzzy learning" that fills up the white spaces in the classroom activities is either irrelevant or somehow handled better online.
Oh, and we assume that it all works, technically and pedagogically, because nobody tests software fully before it gets to the customer :-)