There are quite a few different libraries out there that can help with measuring your Site Speed, specifically Google’s Core Web Vitals standards. The primary three tools that are are commonly used and set the standards are web-vitals, Lighthouse, and PageSpeed Insights. Each tool/library in the list is connected to the one before it.
Lighthouse is the name of the tool created by Google to collect many site speed metrics, as well as some SEO and accessibility data. It also collects Core Web Vitals. Lighthouse runs attached to a browser, and by default can be run on a headless version of Chromium (meaning you can run it on a server to create reports). The CLI version, for example, allows you to generate reports from the command line on your own computer, and can output to different formats, including as a visual HTML report.
Lighthouse also provides a standard scoring system.
Google PageSpeed Insights is a cloud hosted version of Lighthouse. Where Lighthouse requires someone to host the server or computer running the Lighthouse report, PageSpeed Insights provides the hosting and backend, allowing anyone to use the hosted tool and let Google’s server run the report. It’s virtually identical to Lighthouse in the final report, with the exception of “Lab Data”, which is Google’s field data extracted from users using Chrome to visit the page over the last 30 days (the same data that Google Search Console uses).
On a side note, those aren’t the only three tools that can be used for site speed. Lighthouse has been around for awhile, even longer than web-vitals and before Core Web Vitals was a thing. Lighthouse has been used to accompany other reporting tools like GTMetrix and WebPageTest, usually to provide a score. More recently, GTMetrix has switched to using Lighthouse as the primary method of data collection rather than their own scanning tool, as Core Web Vitals became a bigger thing. Additionally, WebPageTest now uses the web-vitals library to supplement their own scans.