It can be, but Applied Science is too general a term. It is taking what a bunch of guys are doing in a lab and turning it into something useful that can make a profit. ex. Two guys in a lab were...
Pure science is science done in a laboratory. It is also called natural science. Applied science is also called technology or engineering. It is done outside. In pure science, a biologist might...
It depends on the institution, while generally equivalent; many colleges will vary in their "in"'s and "of"'s. A local state college in Florida offers the following program: