There are many differences among these 5 schools, a number of which have already been pointed out by other posters.
Richmond was once a very southern school, a place where Virginia’s old money sent their kids. But that has changed dramatically. It has become very popular with Northeners. Today the majority of the students come from the East Coast in the DC-Boston corridor to the north of Virginia. In this respect it is different from any of the other schools on your list.
Vanderbilt is the only one with a truly national population. Washington & Lee, Wake Forest, and Davidson all draw the majority of their students from states of the Confederate South.