Client-side time is the time zone that the person who's loading the page is in. It's based off the local time that their computer is set in.
For example if someone loads an article at 12:00pm (EST) in New York City, their client-side time is 12:00. At that same moment, someone in London would load that page at 5:00pm (BST) and their client-side time would be logged at 5:00pm.
UTC is a standardized way to denoting time across all time zones. It's used pretty interchangeably with Greenwhich Mean Time. When you use UTC time it's up to you to do the time zone math.