Spiller is playing structured games like board games, or sports, while leger is more like free play outside, running around, or what animals do.
Ah that makes sense, we use 'to lake' in the north of England to mean the same thing which probably has the same root.
In the southern parts of England people use the term "lark around" which, according to the internet, derives from the Yorkshire dialet "lake" which is the same as you described.
Would "spiller" also be used if someone wanted to say they played a musical instrument?
Yes. "Jeg spiller klaver" = "I play the piano" (though in Danish it's not the definite we use as it is in English. klaver = piano, klaveret = the piano)
Is 'Jeg spiller fløjte' correct? Because I play the flute and really want to be able to say I do in Danish.
So Danish 'spiller' and 'leger' are to the Swedish 'spelar' and 'leker', respectively?
In another thread, commenters have said that ‘spiller’ needs a direct object, so that this sentence sounds incomplete (whereas ‘leger’ would do fine here).
Danes will never admit it, but there are many similarities, especially in the vocabulary. The Nordic languages have borrowed many words from Plattdeutsch, that is the variety of German spoken in the North (Hamburg, Luebeck, etc.); that explains the many differences in vocabulary between Icelandic/Faroese and Danish/Norwegian/Swedish. As far as grammar is concerned the similarities are due to their all being Germanic languages.
I'm a Danish native speaker, and I'm use the Danish Duolingo course just to be sure that I won't forget my English, but every time there's been an exercise in which it asked me to translate a sentence with the pronoun "we" in it, i've been mean to hear the speaker pronounce the Danish pronoun "vi" like "vi's" or "vies" which isn't the right pronounciation because it should just be pronounced "vi" without the extra "s" sound at the end. Is it just me, or are there other native speakers who have experienced the same? Does the female speaker really say "vi's" or "vies" in stead of just saying "vi"?