Yes, you can use your youtube adsense account in your website. You do not need to apply for another Google Account. Remember you cannot create more than 1 account using 1PC and 1 address.

Now I will tell you step by step how to use youtube adsense account in your website?

Requirements:

* 1st you need to create a website by using a top level domain
* You should create your website by abide by the rules of Google webmaster tools  guideline, Google search friendly site, Steps to a Google-friendly site.
* Your website must be mobile friendly according to google. You can test your site by using this mobile friendly test tools.
* Your website must have more than 50+ post with 350+ words per post. and 1000+ visitors per day.

Now lets we see the steps of applying of youtube adsense Account.
* Go to your youtube adsense account
* Go to settings and then clock on site management
* Now add your website and apply for Google Adsense.
* Your website must have www. As for example – www.itinfoworld.com 

I think you have got your answers. Thanks for your questions.