I just changed jobs, so I still have some of the contract language fresh in mind. The it's spelled out in my contract (which i not unusual in terms of the danish labor market) is that I must call in sick, if I'm too sick to go to work. If I'm going to be sick for more than a few days (i.e. it's not just a flu or something) I have to get a note from a doctor (I think the company pays the expenses). Finally they are entitled to let me go if I'm sick for more than 120 days in a row.
Besides that there are specific allowances for the first day your child is sick (you get to treat that like you were sick yourself) and pregnancies (I can't remember how much time I get of for that, but even as the father I would get a number of weeks with pay).
But the short version is that sick leave is not a set number of days, but the number of days in a given year that I'm sick (which could be zero). And that has absolutely nothing to do with the six weeks of annual payed vacation time I get.
Since I spent by far too long tracking it down - if you need this on Windows, AllChars (http://allchars.zwolnet.com/) does the job nicely.