I'm going to answer this in English, but from what I understand they are somewhat the equivalents of "error (sometimes flaw)" and "mistake" in English. The way I conceptualize it is like "an (error) that I've made is a (mistake)" or "Jeg tog fejl. Det var en fejltagelse." The word fejltagelse almost implies that you've "taget fejl." You've "made an error." You can almost use it as we would in English: "Buying that is a mistake," etc. Again, they are synonyms generally, but you might only be able to use "fejl" when talking about flaws in a machine, system, or plan. You wouldn't really have a mistake in your plan. I think this is the same in Danish. HOWEVER, I've only studied the language for a bit over a year, but here are some links to help you figure it out a bit if native Danes don't respond. http://ordnet.dk/ddo/ordbog?query=fejltagelse http://ordnet.dk/ddo/ordbog?entry_id=11012623&query;=fejltagelse http://ordnet.dk/ (For examples use Korpus link at this site: great resource to learn how words are used in writing) Hope this helps!