The main diffrence between them is if the loop is formed 
between 1 fact table and 2(0r) more dimensions tables,then 
create an alias for existing dimension tables.if loop 
constitute more than one fact table then in this case go 
for contexting.

Contexts and Aliases are means to resolve loops/traps in 
universe designs. Contexts are used to specify which of the 
paths should be used when more than one path is possible 
from one table to another in a loop. Contexts are used in 
the scenarios where two or more many-to-one joins converge 
on a single table. Whereas Aliases are used to resolve the 
loops by duplicating the table and defining separate paths 
when one-to-many join links to a table which is again 
linked to another one-to-many join.