Do I need to apply to Adsence to put ads on one of my other sites? I have adsence on one site already.
You can have AdSense on any websites using a single account as long as the website is not violating AdSense's TOS. It's AdSense but not adsence by the way.
It's not only that you do not need an additional account, you are not even allowed to have one. I was told this very clearly when I inquired because I was in need of two different sets of competitive ad filters - that's a no-go Rainer