Could you tell me what is the slight difference in meaning between the following senences?
It'll take us four hours to get to the coast, so you can sleep while I drive.
It'll take us four hours to get to the coast, so you can sleep while I am driving.
It'll take us four hours to get to the coast, so you can sleep while I drive.
Here, while can (but does not necessarily have to) mean whereas.
If said alone without more context, I would interpret it as "I will drive for the full four hours whereas you can sleep."
It'll take us four hours to get to the coast, so you can sleep while I am driving.
Here, while here can only mean during the time that. The progressive emphasizes the time period when I am driving.
For example, it can be used for this scenarios: I will drive for the first two hours, during which time you can sleep, but afterwards, you will drive instead.
But there are also scenarios where they both make sense.
As has been pointed out, in some contexts, while can mean whereas / on the other hand / contrariwise. But no native speaker would interpret OP's cited example like that without a couple more words to make it obvious exactly where the contrast lies (between what speaker and addressee are able to / must do)...
1: ... so you can sleep, while I have to / must drive
So in practice, while in OP's example only really has the "literal" sense of at the same time / concurrently. I must admit I find it hard to imagine any native speaker using the non-contracted continuous form in this example. But arguably in and of itself the continuous form...
2: ... so you can sleep while I'm driving
...emphasizes the "duration" and/or "immediacy" of the activity (it's a long drive, either already started or starting very soon).
In short, a speaker might use the continuous form for one or more of the reasons given above (by implication, including the possibility that what speaker actually means is ...while I continue driving). But most likely the speaker wouldn't be consciously aware of any of these factors - both verb forms are perfectly natural in the context, and I don't think many native speakers would give any particular thought to the choice here. They're effectively equivalent.
In most cases there will be no difference in meaning between the two phrases. They both can be used interchangeably to indicate that you may sleep while I sit behind the wheel of the vehicle and pilot it. Identifying subtleties of meaning may be insightful but they cannot interpreted to establish any type of rule. Zhantongz's answer does illustrate one of those subtleties.
If you were currently driving and I wanted to indicate that I wanted you to stop driving and allow me take over, I would be more likely to use the active construct, "You can sleep while I drive." However, "while I'm driving" would also work just as well and be completely understood in context.
This is really a question about verb tense, and I'm surprised no one has really given an answer that clarifies the difference between the two in general. English has present tense (sleep) but also a "present imperfect" tense (sleeping). They are very similar, but present imperfect is for actions that are continuous, or unfinished.
It's probably more common than present tense, honestly, especially when talking about things people do, because they can be changed. If I'm talking whether the plumbing in my house works, I might say "the water runs" because at the current moment, it can, and if I turn it on, it does. But if I'm talking about accidentally leaving the faucet on, I'm more likely to say "the water is running" because it is a present state that is likely to change at some point but has not yet stopped.
In the case of "you can sleep while I (drive / am driving)", as others have pointed out, the meaning doesn't really change. I do believe there is a very subtle difference though, which is whose action the tense puts the focus on. "While I am driving" is a continuous, unfinished activity, whereas "while I drive" is more of a discrete single-event action. So, to me, "you can sleep while I drive" puts the focus on the sleeping person, because to them, the driving happens while they're asleep with no observable time elapsing during the drive; but "you can sleep while I am driving" puts the focus on the driving person, because to them, they have to make a continuous effort that won't be finished for a while.
As others have said, there's not really much difference. However, I would say "you sleep while I drive" to mean the other person could sleep the whole way, but "you sleep while I'm driving" to perhaps imply that I'll wake you up when I stop for gas/food/whatever.
If the conversation has been focussed on the other person's need to catch some zees, the "you can sleep while I drive" construction would be the more natural option.
"While I'm driving" emphasises the passenger's freedom to do as they please during the time interval in which the speaker will be focussed on the driving task. But it would be more natural to say something like "OK, I'll be driving, so you can..."
Here's a slightly different example:
"I need you to be quiet while I drive."
"I need you to be quiet while I am driving."
The first sentence states a general rule, the second would be uttered when driving is happening right now and the rule is being broken.
