Direct of Asset Management for Multifamily

In order: 

1. Not to be flippant here, but a Director of Asset Management would direct a team of asset managers. The various asset managers would report to the director. 
2. Student Housing is typically separated from Multifamily because it is handled differently and typically different groups build, manage, sell, and buy Student Housing properties versus traditional multi. Markets are different, strategies are different, teams are different, cap rates can be different, etc. You don't run a student building like you run a multi building and vice versa either. 
3. A senior asset manager is typically just an asset manager who has been there a couple years but still does hands on asset manager work. A director of vice president would run a team, either a small team like a product group or regional team, or the entire team. Amusingly, it genuinely depends on the company if Director is higher than Vice President or vice versa. 
4. Asset management is not unique in having different positions. Tons of industries, particularly in financial roles, have analysts, associates, directors, vice presidents, etc. signifying level and seniority. It is honestly a bit odd to expect asset management to be any different.