Great question! The answer depends on the culture of the person using the word and on the context of the conversation.
In the US, for most situations, they are almost synonymous. However, we do tend to use them a little differently. For example, "I went to college at Yale University." College here refers to the experience of receiving higher education and university is used as part of the proper name of the school.
A college might also refer to a community school or a department of a university. University is usually used to refer to or ask about the specific name of an institution. Americans would rarely say, "I'm going to university" or "He's away at uni (short for university)."
In other English speaking countries, they are not synonymous and asking "Where did you go to college?" might be considered an insult. The person may think you are suggesting that they are not talented, intelligent, or studious enough to attend a "proper university."
When in doubt, use "university."
I hope this helps! :)