Emile de Maat
No, there is no difference between a player engaging an enemy and an enemy engaging a player.
This has been answered in the FAQ:
Lord of the Rings FAQ version 1.7, section 1.49 wrote:
When a player engages an enemy, that enemy has also engaged him, and when an enemy engages a player, that player has also engaged that enemy. There is no difference between engaging an enemy and being engaged by an enemy.