Is there a way to sync a computer to an Apple TV to get the content without having the same apple Id or iTunes account?
Sorry I'm sure this has been answered but I cannot find the information anywhere.
If you want to be able to use iTunes Match for Music, or stream purchased iTunes TV & Movies direct from the cloud, then you have to use the Apple ID that you purchased them under. Also, for movie rentals, you need an Apple ID with a credit card (or gift card balance) connected.
If you only want to stream iTunes content that is already purchased and downloaded to iTunes on your computer, you can do this with Home Sharing. You have to set up Home Sharing with the same Apple ID on both the ATv and iTunes on the computer, but it DOES NOT have to be the same AppleID you use for purchases.
Personally, I want to use the same AppleID for Purchases, because I use both the ATV interface and the iTunes interface to buy things, and I want them all to be under the same account. However, if you prefer, you could set up different iTunes Store accounts in iTunes and ATv, but still use a common Home Sharing account. This would let you buy/rent from either device using seperate accounts, but still share the iTunes content to aTV. You would not be able to get content you purchased through ATV back to iTunes though.