I don't really know the differences between the three roles.
It is more damage in one than the others, more tanky, or is it the champ who makes the difference?
I read this question about what defines a bruiser,
But it makes me even more confused between the three.
Best Answer
There is no definite answer as far as I can see. Most of the namings are from different games or communities. I think you can use the following information as a guideline:
Bruiser
Targets damage towards enemy carries primarily and uses their skills to get to that carry and tie them up.
Off-Tank
Does some damage, but is primarily there to tie up anyone who is trying to mess with their team's carries. They are primarily used as an additional sink and to pick up enemy bruisers who make it past the tank.
Tanky DPS
Pretty much an in between of both bruiser and off-tank.Can take a hit and not have to burn flash to live. They can put out respectable damage as well but not enough to really be a threat to most tanks. A lot of characters can fit into any of these roles depending on how they are itemized.
Examples:
Jarvan with Trinity Force is more bruiser. Jarvan with Frozen Mallet and Randuin's is more off-tank.
An other explanation I found on Reddit: