My professor claims that inserting the same key into a hash table again will lead to a collision … – Is he really right? My whole life I thought 


  a collision is a situation that occurs when two distinct pieces of data have the same hash value.


Everything looks a little bit different now: A few days ago we had to analyse common collision resolution strategies to handle the event that at least two keys being hashed to the same slot of an ordinary hash table. As mentioned above, to my knowledge (as well as my intuition) when inserting the very same key $k$ – that is already assigned to a slot of a hash table $T$ – again,  nothing (special) happens and $T$ remains unchanged.

I wonder now, if i misunderstood this basic concept, since my professor claims, that inserting the key $k$ into a hash table $T$ again will lead to a collision anyway and we have to analyse some collision resolution strategies in this case too …

Many thanks in advance for your help and clarification!
I suppose one could define the word however you like, but I've always understood it to mean the same thing you are talking about. Here I'm assuming if you try to insert a key the second time, no change is made, as it is already present.  If inserting the key caused a second copy to be inserted somewhere, then I think it's more ambiguous and in any formal analysis it would be best to define precisely what you mean by a collision and state whether you consider that a collision, to avoid confusion.