These may sounds the same, but do they really mean the same.
Some smart English teacher might disagree with me, or might wanna argue with me, well you are more than welcome.
Anyway, from my understanding, Holding On, is like, eerrm Holding On, i.e. Lewis is still holding on to what his mentor had taught him, not to flirt with danger.
While, Hold on tight, is like, when the bus driver tried to overtake the Nissan Skyline, he asked the passenger to Hold-on tight, so that they will not be thrown over board.
Then Holding Tight, is holding, grasping something tightly.
So Hold-On, what does the above photo represent, neither, the hands are actually stroking the arrows!