What is the difference between the anachoice screen and the ANA screen, ifa? The first one came back positve, but the second came back negative.

IFA better. For a screen the ifa is much better. It is the gold standard. The ANA choice is not a screening test and should not be offered as a screening test. Your question is somewhat counter intuitive. The ifa is a better test and if choice is positive - it can be subseted into 12 antigens and the lab can tell you. I would follow your test results with ANA subsets per your rheumatologist.
Different methods. Different methods of doing a lab test will some times give different results. If one of the tests is negative, it is unlikely that you are at high risk of having a disease associated with anti-nuclear antibodies. It would be prudent to repeat the test in about a year, especially if you continue to have symptoms that prompted the test in the first place.