In the US, I’ve heard it called shaved ice/snow cone if it’s freshly ground ice with flavor added by a person, popsicle if it comes in a single serving, and sorbet (often pronounced “sherbert”) if it comes in a tub. Usually sorbet tastes the most uniform and has the softest texture, but shaved ice at the County Fair on a hot sunny day hits like nothing else! (Also hits your wallet like nothing else too but that’s event pricing for ya)
Sometimes we call the squeeze tubes otter pops but I’m pretty sure that’s a brand name we use as a generic term.
I don’t disagree that they’re different terms, but I personally know a bunch of people who buy sorbet and call it sherbert, and basically use the terms interchangeably