So in California, and maybe I am wrongly assuming the rest of the United States, people are always asked what college do you attend or what college are you planning on going to.
I found that the difference in the definition between college and university is that colleges don't offer graduate programs, but most people don't distinguish between the terms. College = University to most people and I'm trying to understand how that came to be.
I can't directly answer about the etymology of the word, "college", but I'd like to point out additional uses and contexts for the word in the USA.
Most USA Universities are composed of multiple colleges such as
Note: Some universities like Stanford use the term, "School", interchangeably with "College": https://www.stanford.edu/academics/schools
In the last few decades, it has been common for universities to create a college named "University College" (https://ucollege.wustl.edu) or something similarly non-specific which is a financial accounting unit for collecting fees etc. from students who have not declared a major concentration of study and perhaps students who are in special honors programs. It's another way the University keeps track of money.
In USA University governance and finances, the various colleges often operate semi-autonomously. Each college has a profit and loss statement. Each college reports its own enrollment statistics. It's common for colleges to nominate members of a "Faculty Senate" that may be responsible for ratifying polices that apply to the entire university. Faculty Senates also may interview and recommend candidates for senior administrative positions in conjunction with a "Board of Regents".
Each college will typically have a Dean and possibly Assistant or Associate Deans. Deans are like company Vice Presidents. They are responsible for enrollment and financial operation of a college or major/visible organization within the university. There may also be positions like "Dean of Student Affairs" or "Dean of Enrollment" or "Dean of Minority Outreach", etc. The Deans all report to a Provost and or University President.
A "Board of Regents" is like a corporation's "Board of Directors" and is usually composed of retired politicians, large donors, and community/business representatives. The "Board of Regents" loosely oversees university operation, endowments, research institutes, affiliations with other universities, etc. If a University President or Provost is going to be fired, it is the Board of Regents who do the firing.
The founders of the first American schools of higher learning in the 17th century, such as Harvard College, were educated at universities such as Cambridge and Oxford. These new world schools were not felt to be comparable to a European university, as they were uni-disciplinary and did not grant higher degrees in fields like medicine. Harvard was simply a college of theology in the beginning. These schools were much smaller, and were organized more like the residential colleges that made up the larger universities they were accustomed to in Europe. Over time, these colleges grew, some sprouted other faculties and colleges, and, particularly in the 19th century, there was a push to organize like British universities (as Harvard did). However, the word "college" stuck in America as a generic name for a post-secondary institution of learning.