To "enter" generally refers to a student's initial attendance at a school as a function of age, eg "the boy was too young to enter college." As noted, it may also refer to the physical, literal entrance into a school building.
"To attend" refers to school attendance at any time, whether it is the student's first or tenth year to do so, eg "He received money to attend college."
There are contexts where the distinction might be less evident, but this generally illustrates the difference in the expressions.