What does UI stand for in NYS Department of Labor unemployment context?

Yes, UI stands for Unemployment Insurance. It's the official term for unemployment benefits in New York. You'll see it used interchangeably with 'unemployment benefits' on the NYS Department of Labor site and in official correspondence. Don't worry about the acronyms too much - as long as you're filing your weekly claims correctly and meeting the job search requirements, you're on the right track.

ui = unemployment insurance, but theres also tons of other abbreviations like WBR (weekly benefit rate) and stuff that they dont really explain anywhere

The NYS Department of Labor uses a lot of technical terms that can be overwhelming at first. UI (Unemployment Insurance) is the basic program, but you might also see references to adjudication (when they're reviewing your claim), job search requirements (the work search you need to do each week), and various claim statuses. If you're having trouble navigating the system or need to speak with someone directly about your claim, I had success using Claimyr (claimyr.com) to get through to an actual NYS Department of Labor agent. They have a video demo at https://youtu.be/qyftW-mnTNI that shows how it works.

honestly the whole system is designed to confuse people with all these acronyms and technical terms. they make it so complicated on purpose

UI is just unemployment insurance like everyone said. Once you get used to the system it's not too bad, just make sure you keep up with your weekly claims and job search log!