A difference equation is a recurrence relation where the current element $y[n]$ of a sequence is related to its past values $y[n-k]$, $k>0$ (if we interpret the index $n$ as time index, which is not necessary). The equation you gave in your question is a special case, because there are no past terms $y[n-k]$ involved, so you could call it a zeroth order difference equation, but you're right that from a common sense point of view it is no difference equation at all.
However, what counts here is the fact that no past (or future) elements $y[n-k]$ are involved, and not that "nothing is getting subtracted". E.g., the following equation is a standard example of a difference equation:
The subtraction takes place in the index $n$ ($y[n-1]$). But obviously you can substitute $n+1$ for $n$ yielding
which is completely equivalent to $(1)$ with no subtraction taking place, but it's still a difference equation, because the difference between the indices remains unchanged.