It's in the sense of applying for e.g. a position or a scholarship, so it could be request in some cases - like a request for a grant. But it's not a demand and it's certainly not solicitude, did you mean another word?
I think that is less specific. You can request just about anything but you can only apply for certain things.
- application = applikation
- applications = applikationer
- app = app
- apps = appar
- software = mjukvara
So quite similar. :)
I did some digging and found that: att ansöka = to apply en ansökning = an application, but also an alternate spelling of "ansökan". Maybe it's an older/archaic word, formal vs. colloquial? Is this word used as much as ansökning and does it have any particular conditions in which it can/should be used? As is the case with some previous words I've learned.
They're synonymous; ansökning fell out of use at one point but appears to be coming back into Swedish, so both are correct and fine - but ansökan is usually the better choice at the moment.