There are three levels of application in the US.
1° freshman, or first time in college. This is for students who have not started at a university (they can have enrolled but not attended; they can have taken supplementary classes when they were in high school, but only before they graduated). Some universities also consider students with fewer than 15 credits as “freshman applicants”. These form the majority of places offered. Generally, you apply to the university or sometimes to a college within the university, not to a department. In fact you’re not even expected to apply to a specific field of study.
2° transfer students. They have enrolled in a university and taken classes there; they have grades. There are fewer places for transfers, since they’re places the freshmen who didn’t succeed have created when they let the university. Some large public universities do “save” places for transfers who live in their state and attended community college in their state. They need to know what field of study they want to graduate in and they must have taken “pre-requisite” courses. Pre-reqs are classes that form a background to more specialized study.
Freshmen and transfers apply to the university but freshmen can indicate “undecided” or 2 different fields of interest.
3° graduate students. They have graduated from college, with a 4-year degree. They apply for a Master’s degree or PHD. They apply directly to a department.