It seems that you have already answered your question somewhat, but I will talk about what you mentioned.
Karma is a test framework that is largely agnostic for language tests. It has a rich ecosystem of plugins that lets you pretty much customize how and when your tests run.
To test Javascript, we often need to test against the implementation of the DOM. There are many plugins that allow you to connect to various browsers, such as karma chrome. These plugins load the required browser and run your tests against the browser.
However, there are times when you want to run without a physical browser installed in the target test field. this is where PhantomJS comes in. This is a headless browser that can be launched without being installed on the target machine. He cannot replace karma. If you want to describe him as a "competitor", he will be a competitor to IE, Firefox, Chrome and Safari.
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