'While' can actually be all of those things, and more (the following comes from the OED, sadly I do not know how to paste a screenshot here):
• relative adverb: during which: the period while the animal remains alive
1) during the time thay, at the same time as: nothing much changed while he was away
2) whereas (indicating a contrast): one person wants out, while the other wants the relationship to continue.
3) inspite of the fact that, although: while I wouldn't recommend a night-time visit, by day the area is full of interest.
1) - a period of time: we chatted for a while. She retired a little while ago.
- for some time: can I keep it a while?
2) the while= at the same time, meanwhile: he starts to draw, talking the while.
• preposition: until: father will be happy while dinner time.
• verb (transitive): (while something away) pass time in a leisurely manner: a diversion to while away long afternoons.
I was wondering that, too. I think if you look at direct translation it makes a bit more sense when to use either one.
'She drinks while she works' 'She drinks during she works.'
I'm not sure what this structure is called, but if you use another verb at the end of the sentence, it seems to work better with terwijl, and if using a noun tijdens works better.
'She drinks during work'
'During' is a preposition, and as such, it can only be followed by a noun or a noun phrase.
Thus, 'she drinks during work' or 'zij drinkt tijdens het werk' (though it sounds a bit odd...).
'While' can be a preposition, but also a relative adverb and a conjunction (among other things, check my previous post), and as such, it can precede a clause.
Therefore, you'd say 'she drinks while she works' or 'zij drinkt terwijl zij werkt' (which in a way sounds more natural).