The live testing option helps you debug your website in real time. So, it enables you to interact with a browser running on a real device. Live is ideal for manual testing either during nascent stages of a project or when you introduce new features.
Automate is of use when you have defined the standard tests that you would like to include as a part of your suite. Automate works through the remote version of Selenium for the cloud. It supports major CI/CD tools like Jenkins and Travis CI.
After registering for BrowserStack, you get 100 minutes of free testing, after which you have to opt for a paid plan. Monthly plans start at $29/mo. Recently, BrowserStack has introduced a pay as you go plan based on the minutes that you use.
LambdaTest is another tool in the cloud for cross browser testing that lets you either perform tests live or automate them through Selenium in the cloud. For a real test, you can select a combination of device + browser. The tool will then initiate a session where you can interact with a browser in real time. You have over 2,000 real devices available to test.