No. It was the same language. Livewire was the server tech. Livewire implemented a tag in LiveScript, but the majority of the scripting implementation was exactly the same. [0]
JS was originally named Mocha, but it was renamed to LiveScript as a tie-in with the server tech. However, after the deal with Sun Microsystems to put Java in the browser, it was almost scrapped before being saved by giving it the final name of JavaScript. [1]
To clarify, there was around a fifteen year gap between Livewire and Node.js, so things were not quite as streamlined as you implied.
JS was originally named Mocha, but it was renamed to LiveScript as a tie-in with the server tech. However, after the deal with Sun Microsystems to put Java in the browser, it was almost scrapped before being saved by giving it the final name of JavaScript. [1]
To clarify, there was around a fifteen year gap between Livewire and Node.js, so things were not quite as streamlined as you implied.
[0]: https://dev.to/macargnelutti/server-side-javascript-a-decade...
[1] https://www.oreilly.com/library/view/node-up-and/97814493322...