Wikipedia wrote:

The origin of the U.S. usage

The founders of the first institutions of higher education in the United States were graduates of the University of Oxford and the University of Cambridge. The small institutions they founded would not have seemed to them like universities — they were tiny and did not offer the higher degrees in medicine and theology. Furthermore, they were not composed of several small colleges. Instead, the new institutions felt like the Oxford and Cambridge colleges they were used to — small communities, housing and feeding their students, with instruction from residential tutors (as in the United Kingdom, described above). When the first students came to be graduated, these "colleges" assumed the right to confer degrees upon them, usually with authority—for example, The College of William & Mary has a Royal Charter from the British monarchy allowing it to confer degrees while Dartmouth College has a charter permitting it to award degrees "as are usually granted in either of the universities, or any other college in our realm of Great Britain."

The leaders of Harvard College (which granted America's first degrees in 1642) might have thought of their college as the first of many residential colleges which would grow up into a New Cambridge university. However, over time, few new colleges were founded there, and Harvard grew and added higher faculties. Eventually, it changed its title to university, but the term "college" had stuck and "colleges" have arisen across the United States.

In U.S. usage, the word "college" embodies not only a particular type of school, but has historically been used to refer to the general concept of higher education when it is not necessary to specify a school, as in "going to college" or "college savings accounts" offered by banks.