TL;DR
The main difference lies in where the master and dev branches end up pointing.

Full explanation
Merging one branch into another is not a symmetric operation:
- merging
devintomaster, and - merging
masterintodev,
are, in general, not equivalent. Here is an illustrative example that explains the difference between the two. Let’s assume your repo looks as follows:

If you merge dev into master
If master is checked out (git checkout master),

and you then merge dev (git merge dev), you will end up in the following situation:

The master branch now points to the new merge commit (F), whereas dev still points to the same commit (E) as it did before the merge.
If you merge master into dev
If, on the other hand, dev is checked out (git checkout dev),

and you then merge master (git merge master), you will end up in the following situation:

The dev branch now points to the new merge commit (F', whereas master still points to the same commit as it did before the merge (D).
Putting it all together
