My husband and I moved from NYC in August 2007 to Seoul. We plan to be here for at least a year. I'm going back in August 2008, my husband will probably return sometime in 2009. I made my money in 2008 in NJ. My husband made some in NYC. We were told that we are not part-time residents because we plan to go back to New York and we must pay full year resident NYS/NYC taxes. We will be moving back to our same rented apt (it is being subletted now).
Also, we took the moving credit because I am doing work in Seoul (for the same NJ company).

We're very confused so any help would be greatly appreciated.

There is no Yes or No answer in your case.
Since your visit outside NY is temporary, the state may want to tax even your foreign income.
To be safe you should file state tax return for 2007 and 2008 even if you file as part year resident or nonresident (showing any income from NY sources). In this way, state has a 3-years time limit to question you.