What is the difference between a school and a college within a university?

Hi, I was looking at a post you made where you called Barnard and Columbia, both LACs. Barnard is more commonly referred to as a LAC and Columbia College not. I started a thread several weeks ago asking What is Liberal Arts School? When I first started my research for my older son, I had a different impression of a Liberal Arts School is. I found it misleading that if my kid went a LAC, they would automatically emphasize Liberal Arts.

Is Harvard College a LAC? For example, if you’re enrolled at the College of Arts and Science at Wash U and studying history, are you in a Liberal Arts College? If you’re enrolled at the College of Management at Bucknell University studying accounting, are you in a Liberal Arts College?